Question

Rahul went to excursion along with his friends. He saw a tower stands vertically on the ground . He observes that from a point on the ground, which is 15 m
away from the foot of the tower, the angle of elevation of the top of the tower is found to be thita
such that cos thita= 0.5. Find the height of the tower.​

Answer 1

The height of the tower which is 15 m away from a point subtending 60 degrees to the top of the tower is 25.98 m.

Step-by-step explanation:

Referring to the figure attached below, let’s make some assumption

AB = h = height of the tower standing vertically on the ground

BC = 15 m = the distance of the foot of the tower from the point C

θ =  angle ACB = the angle of elevation of the top of the tower

It is given that cos θ = 0.5 ∴ θ = 60°

Considering ∆ABC, applying the trigonometric ratios of a triangle, we get  

tan θ =   $\frac{perpendicular}{base}$

⇒ tan 60° =   AB/BC

⇒ tan 60° = h/15

⇒ √3 = h/15

⇒ h = 15√3  

⇒ h = 25.98 m

Thus, the height of the tower is 25.98 m.

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Also View:

The angle of elevation of the cloud from a point 60m above the surface of the water of a lake is 30 degree and angle of depression of its Shadow from the same point in a water of lake is 60 degree find the height of the cloud from the surface of water .

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Angles of elevation of the top of a tower from two points at distance of 9 m and 16 m from the base of the tower in the same side and in the same straight line with it are complementary. Find the height of the tower.

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Answer 2

Answer:

This answer is very lengthy