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Applications of Trigonometry || Quantitative Aptitude || CAT 2021 || 04 June

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Question 1

If sinθ – cosθ = , then find the value of sinθ.cosθ.

Question 2

When the angle of elevation of the sum increases from 30° to 60°, the shadow of a pole is diminished by 5 meters. Then the height of the pole is :

Question 3

If sin(x + y) = cos(x – y), then the value of cos2x is:

Question 4

The distance between two vertical poles is 60 m. The height of one of the poles is double the height of the other. The angles of elevation of the top of the poles from the middle point of the line segment joining their feet are complementary to each other. The heights of the poles are:

Question 5

If cos4θ - sin4θ = 3/4, then the value of 2cos2θ – 1 is:

Question 6

The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.

Question 7

If , then, what is the value of sin(α+β)?

Question 8

A person observes the angle of elevation of a building as 30 °. The person proceeds towards the building with a speed of  . After 2 hours, he observes the angle of elevation as 45 °. The height of the building (in meter) is?

Question 9

The maximum value of 3 cosx + 4sinx + 8 is

Question 10

From a point 12 m above the water level, the angle of elevation of the top of a hill is 60° and the angle of depression of the base of the hill is 30°. What is the height (in m) of the hill?
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