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

Approximate height of the building is 23213 meters.

Step-by-step explanation:

Let the height of the building be represented by h.

0.02 radians = 0.02 ×
`(180^(o) )/(\pi )`

= 0.02 x (180/
`(22)/(7)`)

0.02 radians = 1.146°

10.5 km = 10500 m

Applying the trigonometric function, we have;

Tan θ =
`(opposite)/(adjacent)`

So that,

Tan 1.146° =
`(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.