Question

The apparent height of a building 10.5 km away is 0.02 radians. What is the approximate height of the building to the nearest meter

Answer 1

Answer:

Approximate height of the building is 23213 meters.

Explanation:

Let the height of the building be represented by h.

0.02 radians = 0.02 × $\frac{180^{o} }{\pi }$

                     = 0.02 x (180/$\frac{22}{7}$)

0.02 radians  = 1.146°

10.5 km = 10500 m

Applying the trigonometric function, we have;

Tan θ = $\frac{opposite}{adjacent}$

So that,

Tan 1.146° = $\frac{h}{10500}$

⇒ h = Tan 1.146° x 10500

      = 2.21074 x 10500

      = 23212.77

h = 23213 m

The approximate height of the building is 23213 m.