flag pole casts a shawdow 27.7 ft long when the sun has a angle of elevation 38 degrees, to the nearest tenth of a foot, how tall is flagpole?

Question

must draw a picture and find how tall the flagpole is. 

Answer 1

Let h be the height of the flagpole (in feet). The shadow and the flagpole form a right triangle with the right angle at the base of the flagpole. The hypotenuse of the right triangle extends from the tip of the shadow to the top of the flagpole. (I must describe this using words, because I cannot draw a picture in this chat box.)

 

The base of the triangle has an angle of 38° with the hypotenuse, and the length of the base is 27.7 ft. To find the height, you must use a trigonometric ratio which involves both the side adjacent to the angle (27.7 ft) and the side opposite the angle (h). This is the tangent ratio.

 

tan 38° = h/27.7 .

 

Multiply both sides by 27.7 and then calculate the answer using a calculator set to degree mode.

 

h = 27.7 tan 38° ≈ (27.7)(0.7812856265) ≈ 21.6 ft to the nearest foot.