Question

Robert is lying on the ground, looking at the top of a flagpole. The angle of elevation to the top of the flagpole is

Answer 1

Answer:

Height of flagpole = 571 ft

Step-by-step explanation:

Given:

Angle of elevation to the top of the flagpole is 55° .

Distance from the eyes to the base of flagpole = 400 ft.

To find the height of the flagpole.

Solution:

We can draw the situation as a right triangle as shown below.

In triangle ABC.

$BC=400\ ft$

∠C= 55°

To find the length AB (height of the flagpole).

Applying trigonometric ratio :

$\tan\theta=\frac{Opposite\ side}{Adjacent\ side}$

$\tan C=\frac{AB}{BC}$

Plugging in values.

$\tan 55\°=\frac{AB}{400}$

Multiplying both sides by 400.

$400\tan 55\°=\frac{AB}{400}\times 400$

$571.26=AB$

∴ $AB\approx 571\ ft$

Height of flagpole = 571 ft