Chapter 12 Application Of Trigonometry Math 11th Class Punjab MCQ Tests
11th Class Math Chapter 12 MCQ Tests
Chapter 12 of 11th Class Math has 39 questions. If you take an online MCQ test, the system will randomly choose the questions. If you want to take the quiz by chapter then click the start test button.
Total Questions: 39
Total Marks: 39
Time: 40 Mins
Total Questions: 39
Total Marks: 39
Time: 40 Mins
40Min : 00 Sec Remaining
Question # 1
In a triangle A B C , given that ∠ A = 58 ∘ , ∠ B = 76 ∘ and c = 8 . Find the value of a.
Question # 2
Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30 ∘ and 45 ∘ , respectively. If the lighthouse is 100 m high, the distance between the two ships is:
Question # 3
A person has a kite out on 1750 f t of string at an angle of 75 ∘ with ground. An observer notes that the angle formed by the kite and the flier is 102 ∘ . How far is the kite from the observer?
Question # 4
Solve the triangle A B C in which A C = 105 c m , A B = 76 c m and A = 29 ∘ .
Question # 5
In a triangle A B C , given that ∠ C = 113 ∘ , ∠ B = 41 ∘ and c = 15 . Find the value of a.
Question # 6
Find the length of side a of the triangle A B C , if the area of triangle is 144 cm2 and β and γ are 53 ∘ and 35 ∘ , respectively.
Question # 7
Determine the area of triangle, if r 1 = 6 c m and s − a = 2.
Question # 8
Find the value of:
Question # 9
Find the exact value of:
Question # 10
Find the area of the triangle A B C , if the perimeter is 30 , a = 4 and r 1 = 4.
Question # 11
Find the unknown values in the following figure.
Question # 12
If height of wind mill is 95 m and its shadow is 65 m , then angle of elevation of sun at that particular moment is:
Question # 13
In the diagram below, O P is a painting hung on a wall O Q . S and R are points on the level ground such that O R = P S = 8 m . The angle of elevation of the top frame, O , of the painting from R is 58 ∘ while that of lower frame, P , of the painting from S is 33 ∘ . Find the height of the painting.
Question # 14
Find the length of Y Z.
Question # 15
The formula to find the area of triangle is:
Question # 16
From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of a 20 m high building are 45 ∘ and 30 ∘ , respectively. Find the height of the tower.
Question # 17
An observer 1.6 m tall is 20 √ 3 m away from a tower. The angle of elevation from his eye to the top of the tower is 30 ∘ . The height of the tower is:
Question # 18
The sides of a triangular plot are in the ratio 3 : 5 : 7 and its perimeter is 300 m . The sides of a triangle are:
Question # 19
Find the radius r , if area of the triangle is 60 cm2 and s = 15.
Question # 20
Two houses are in front of each other. Both have chimneys on their top. The line joining the chimneys makes an angle of 45 ∘ with the ground. How far are the houses from each other if one house is 25 m and other is 10 m in height?
Question # 21
If each side of a triangle is doubled, area of the triangle will become _____.
Question # 22
The triangle A B C is _____ triangle.
Question # 23
The angle of depression from the top of a tower 12 m high, at a point on the ground is 30 ∘ . The distance of the point from the top of the tower is:
Question # 24
Product of s i n 61° and t a n 58° upto five significant figures is:
Question # 25
A man standing at a point C is watching the top of a tower, which makes an angle of elevation of 30 degree. The man walks some distance towards the tower to watch its top and the angle of elevation becomes 60 degree. What is the distance between the base of the tower and point C ?
Question # 26
John looks at a tree top and the angle made is 45 ∘ . He moves 10 c m back and again looks at the tree top but this time angle made is 30 ∘ . How high is the tree top from ground?
Question # 27
Evaluate:
Question # 28
A vertical tower is 20 m high from the horizontal ground. The angle of depression of a ball from the top of the tower is 42 ∘ . Calculate the distance, in m , of the ball from the base of the tower.
Question # 29
The formula to find the area of equilateral triangle, with side a, is:
Question # 30
The formula to find the area of equilateral triangle, with side a, is:
Question # 31
A bicycle ramp is constructed for high-level competition with an angle of θ formed by the ramp and the ground. Another ramp is to be constructed half as steep for novice competition. If t a n θ = 5/3 for higher-level competition, what is the measurement of the angle for novice competition?
Question # 32
Find the values of a and b in the following figure.
Question # 33
Value of s i n 62° upto four significant figures is:
Question # 34
Find the ex-radius of the triangle having area of 16 s q . u n i t s and ( s − b ) = 7.
Question # 35
Two houses are in front of each other. Both have chimneys on their top. The line joining the chimneys makes an angle of 45 ∘ with the ground. How far are the houses from each other if one house is 25 m and other is 10 m in height?
Question # 36
In a triangle A B C , ∠ A = 108 ∘ , b = 9 and c = 15 . Find the value of a.
Question # 37
Describe the relation given in the figure.
Question # 38
In the figure below, a = 7 , c = 18 and d = 10 . Use this information to solve the parallelogram for b.
Question # 39
Solve the triangle A B C , by half angle formula, when a = 283 , b = 317 , c = 428.
Total Questions
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Question # 1
In a triangle A B C , given that ∠ A = 58 ∘ , ∠ B = 76 ∘ and c = 8 . Find the value of a.
Question # 2
Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30 ∘ and 45 ∘ , respectively. If the lighthouse is 100 m high, the distance between the two ships is:
Question # 3
A person has a kite out on 1750 f t of string at an angle of 75 ∘ with ground. An observer notes that the angle formed by the kite and the flier is 102 ∘ . How far is the kite from the observer?
Question # 4
Solve the triangle A B C in which A C = 105 c m , A B = 76 c m and A = 29 ∘ .
Question # 5
In a triangle A B C , given that ∠ C = 113 ∘ , ∠ B = 41 ∘ and c = 15 . Find the value of a.
Question # 6
Find the length of side a of the triangle A B C , if the area of triangle is 144 cm2 and β and γ are 53 ∘ and 35 ∘ , respectively.
Question # 7
Determine the area of triangle, if r 1 = 6 c m and s − a = 2.
Question # 8
Find the value of:
Question # 9
Find the exact value of:
Question # 10
Find the area of the triangle A B C , if the perimeter is 30 , a = 4 and r 1 = 4.
Question # 11
Find the unknown values in the following figure.
Question # 12
If height of wind mill is 95 m and its shadow is 65 m , then angle of elevation of sun at that particular moment is:
Question # 13
In the diagram below, O P is a painting hung on a wall O Q . S and R are points on the level ground such that O R = P S = 8 m . The angle of elevation of the top frame, O , of the painting from R is 58 ∘ while that of lower frame, P , of the painting from S is 33 ∘ . Find the height of the painting.
Question # 14
Find the length of Y Z.
Question # 15
The formula to find the area of triangle is:
Question # 16
From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of a 20 m high building are 45 ∘ and 30 ∘ , respectively. Find the height of the tower.
Question # 17
An observer 1.6 m tall is 20 √ 3 m away from a tower. The angle of elevation from his eye to the top of the tower is 30 ∘ . The height of the tower is:
Question # 18
The sides of a triangular plot are in the ratio 3 : 5 : 7 and its perimeter is 300 m . The sides of a triangle are:
Question # 19
Find the radius r , if area of the triangle is 60 cm2 and s = 15.
Question # 20
Two houses are in front of each other. Both have chimneys on their top. The line joining the chimneys makes an angle of 45 ∘ with the ground. How far are the houses from each other if one house is 25 m and other is 10 m in height?
Question # 21
If each side of a triangle is doubled, area of the triangle will become _____.
Question # 22
The triangle A B C is _____ triangle.
Question # 23
The angle of depression from the top of a tower 12 m high, at a point on the ground is 30 ∘ . The distance of the point from the top of the tower is:
Question # 24
Product of s i n 61° and t a n 58° upto five significant figures is:
Question # 25
A man standing at a point C is watching the top of a tower, which makes an angle of elevation of 30 degree. The man walks some distance towards the tower to watch its top and the angle of elevation becomes 60 degree. What is the distance between the base of the tower and point C ?
Question # 26
John looks at a tree top and the angle made is 45 ∘ . He moves 10 c m back and again looks at the tree top but this time angle made is 30 ∘ . How high is the tree top from ground?
Question # 27
Evaluate:
Question # 28
A vertical tower is 20 m high from the horizontal ground. The angle of depression of a ball from the top of the tower is 42 ∘ . Calculate the distance, in m , of the ball from the base of the tower.
Question # 29
The formula to find the area of equilateral triangle, with side a, is:
Question # 30
The formula to find the area of equilateral triangle, with side a, is:
Question # 31
A bicycle ramp is constructed for high-level competition with an angle of θ formed by the ramp and the ground. Another ramp is to be constructed half as steep for novice competition. If t a n θ = 5/3 for higher-level competition, what is the measurement of the angle for novice competition?
Question # 32
Find the values of a and b in the following figure.
Question # 33
Value of s i n 62° upto four significant figures is:
Question # 34
Find the ex-radius of the triangle having area of 16 s q . u n i t s and ( s − b ) = 7.
Question # 35
Two houses are in front of each other. Both have chimneys on their top. The line joining the chimneys makes an angle of 45 ∘ with the ground. How far are the houses from each other if one house is 25 m and other is 10 m in height?
Question # 36
In a triangle A B C , ∠ A = 108 ∘ , b = 9 and c = 15 . Find the value of a.
Question # 37
Describe the relation given in the figure.
Question # 38
In the figure below, a = 7 , c = 18 and d = 10 . Use this information to solve the parallelogram for b.
Question # 39
Solve the triangle A B C , by half angle formula, when a = 283 , b = 317 , c = 428.
Total Questions
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Math MCQ Test by Topics
- +12.1 Introduction
- +12.2 Tables of Trigonometric Ratios
- +12.1 Exercise
- +12.3 Solution of Right Triangles
- +12.2 Exercise
- +12.4 (a) Heights And Distances
- +12.5 Engineering and Heights and Distances
- +12.3 Exercise
- +12.6 Oblique Triangles
- +12.6.1 The Law of Cosine
- +12.6.2 The Law of Sines
- +12.6.3 The Law of Tangents
- +12.6.4 Half Angle Formulas
- +12.7 Solution of Oblique Triangles
- +12.7.1 Case I: When measures of one side and two angles are given
- +12.7.2 Case II: When measures of two sides and their included angle are given
- +12.7.3 Case. lll: When Measures of Three Sides are Given
- +12.4 Exercise
- +12.5 Exercise
- +12.6 Exercise
- +12.8 Area of Triangle
- +12.7 Exercise
- +12.9 Circles Connected with Triangle
- +12.9.1 Circum-Circle:
- +12.9.2 In-Circle
- +12.9.3 Escribed Circles
- +12.10 Engineering and Circles Connected With Triangles
- +12.8 Exercise
Math
- Number Systems
- Sets, Functions and Groups
- Matrices and Determinanls
- Quadratic Equations
- Partial Fractions
- Sequences and Series
- Permutation, Combination and Probability
- Mathematical Inductions and Bionomial Theorem
- Fundamentals of Trigonometry
- Trigonometric Identities
- Trigonometric Functions and their Graphs
- Application of Trigonometry
- Inverse Trigonometric Functions
- Solution of Trignometric Equations
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