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Case Based Questions: Some Application of Trigonometry - Class 10 MCQ


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15 Questions MCQ Test - Case Based Questions: Some Application of Trigonometry

Case Based Questions: Some Application of Trigonometry for Class 10 2024 is part of Class 10 preparation. The Case Based Questions: Some Application of Trigonometry questions and answers have been prepared according to the Class 10 exam syllabus.The Case Based Questions: Some Application of Trigonometry MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Case Based Questions: Some Application of Trigonometry below.
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Case Based Questions: Some Application of Trigonometry - Question 1

Read the following text and answer the following questions on the basis of the same.

A straight highway leads to the foot of tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°.

Q. Write the value of sec 30°.

Detailed Solution for Case Based Questions: Some Application of Trigonometry - Question 1

Case Based Questions: Some Application of Trigonometry - Question 2

Read the following text and answer the following questions on the basis of the same.

A straight highway leads to the foot of tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°.

Q. The line drawn from the eye of an observer to the point in the object viewed by the observer.

Detailed Solution for Case Based Questions: Some Application of Trigonometry - Question 2
The line of sight is the line drawn from the eye of an observer to the point of the object viewed by the observer. The angle of elevation of an object viewed , is the angle formed by the line of sight with the horizontal when object viewed is above the horizontal level.
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Case Based Questions: Some Application of Trigonometry - Question 3

Read the following text and answer the following questions on the basis of the same.

A straight highway leads to the foot of tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°.

Q. Find the time taken by the car to reach the foot of the tower from point D to B.

Detailed Solution for Case Based Questions: Some Application of Trigonometry - Question 3
Let AB be the vertical tower of height h m.

Let the speed of car be v m/s.

Let car takes t seconds to reach the point B from the point D

Distance travel by car in t sec = vt m.

In ΔABD, we have

h = √3 vt ...(i)

and in right D ABC, we have

2vt = 6v

Case Based Questions: Some Application of Trigonometry - Question 4

Read the following text and answer the following questions on the basis of the same.

A straight highway leads to the foot of tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°.

Q. Write the value of cosec 60°.

Detailed Solution for Case Based Questions: Some Application of Trigonometry - Question 4
cosec 60°=

Case Based Questions: Some Application of Trigonometry - Question 5

Read the following text and answer the following questions on the basis of the same.

A straight highway leads to the foot of tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°.

Q. If the two lines are parallel; then the alternate opposite angles are ..................... .

Detailed Solution for Case Based Questions: Some Application of Trigonometry - Question 5
Alternate angles are equal, corresponding angles are equal, co-interior angles are supplementary. Vertically opposite angles are equal. So, all of the options are correct.
Case Based Questions: Some Application of Trigonometry - Question 6

Read the following text and answer the following questions on the basis of the same.

Form a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and angle of elevation of the top of the flagstaff from P is 45°.

Q. Find the distance of the building from the point P.
Detailed Solution for Case Based Questions: Some Application of Trigonometry - Question 6
In right DPAB, we have

Case Based Questions: Some Application of Trigonometry - Question 7

Read the following text and answer the following questions on the basis of the same.

Form a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and angle of elevation of the top of the flagstaff from P is 45°.

Q. What is the value of tan 45°?

Detailed Solution for Case Based Questions: Some Application of Trigonometry - Question 7
Value of tan 45° = 1.
Case Based Questions: Some Application of Trigonometry - Question 8

Read the following text and answer the following questions on the basis of the same.

Form a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and angle of elevation of the top of the flagstaff from P is 45°.

Q. Find the length of flagstaff.
Detailed Solution for Case Based Questions: Some Application of Trigonometry - Question 8
In right ΔPAB

tan 30° =

AP = 10 √3 m

In right ΔPAD,

10 √3 = 10 + BD

BD = 10 √3 – 10

BD = 7.32 m.

Case Based Questions: Some Application of Trigonometry - Question 9

Read the following text and answer the following questions on the basis of the same.

Form a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and angle of elevation of the top of the flagstaff from P is 45°.

Q. What is the value of tan 30°?
Detailed Solution for Case Based Questions: Some Application of Trigonometry - Question 9
Value of tan 30° = 1/√3
Case Based Questions: Some Application of Trigonometry - Question 10

Read the following text and answer the following questions on the basis of the same.

Form a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and angle of elevation of the top of the flagstaff from P is 45°.

Q. Write the Pythagoras theorem for DAPB.
Detailed Solution for Case Based Questions: Some Application of Trigonometry - Question 10
Pythagoras theorem for DAPB is BP2 = AB2 + AP2.
Case Based Questions: Some Application of Trigonometry - Question 11

Read the following text and answer the following questions on the basis of same.

From a point on the bridge across a river the angle of depression of the banks on opposite sides of the river 30° and 45° respectively.

Q. Name the ΔAPD,
Detailed Solution for Case Based Questions: Some Application of Trigonometry - Question 11
ΔAPD is right angled triangle Q

∵ ∠D = 90°

Case Based Questions: Some Application of Trigonometry - Question 12

Read the following text and answer the following questions on the basis of same.

From a point on the bridge across a river the angle of depression of the banks on opposite sides of the river 30° and 45° respectively.

Q. The value of tan 45° is

Detailed Solution for Case Based Questions: Some Application of Trigonometry - Question 12

The value of tan 45° is = 1

Case Based Questions: Some Application of Trigonometry - Question 13

Read the following text and answer the following questions on the basis of same.

From a point on the bridge across a river the angle of depression of the banks on opposite sides of the river 30° and 45° respectively.

Q. If the bridge is at a height of 3 m from the banks, find the width of the river.
Detailed Solution for Case Based Questions: Some Application of Trigonometry - Question 13
In ΔPDA, ∠A = 30°

AD = 3√3m

In ΔPDB, ∠B = 45°

tan 45° = PD/DB

DB = 3m

width of the river = AB = AD + DB

= 3√3 + 3

= 3(√3 + 1)m.

Case Based Questions: Some Application of Trigonometry - Question 14

Read the following text and answer the following questions on the basis of same.

From a point on the bridge across a river the angle of depression of the banks on opposite sides of the river 30° and 45° respectively.

Q. In ΔAPD, tan 30° is
Detailed Solution for Case Based Questions: Some Application of Trigonometry - Question 14
In ΔAPD, tan 30° = Perpendicular/Base

= PD/AD

Case Based Questions: Some Application of Trigonometry - Question 15

Read the following text and answer the following questions on the basis of same.

From a point on the bridge across a river the angle of depression of the banks on opposite sides of the river 30° and 45° respectively.

Q. The value of tangent in right angle triangle is equal to
Detailed Solution for Case Based Questions: Some Application of Trigonometry - Question 15
The value of tangent in right angle triangle is equal to Perpendicular/Base.
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