Question

Jack’s eyes are 5 feet above the ground. He is standing 400 feet from the base of a building. His line of sight forms a 67° angle with the top of the building. How tall is the building?

Answer 1

Answer: 947.34 feet

Explanation:

Hi, since the situation forms a right triangle (see attachment) we have to apply the trigonometric functions.

tan α = opposite side / adjacent side

Where α is the angle that His line of sight forms with the top of the building, the opposite side is the height of the building minus 5, and the adjacent side is the distance between him and the building (400)

Replacing with the values given:

tan 67 = x/ 400

Solving for x

tan 67 (400) =x

x= 942.34 feet

We have to add 5 feet, since we calculated the height of the building minus the eye level.

942.34 +5 = 947.34 feet

Feel free to ask for more if needed or if you did not understand something.

Answer 2

960.7 ft

Explanation:

A right triangle is formed where the distance between Jack and the base of the building is one of the triangles legs and the height of the building plus 5 feet is the other leg (let's call it x). The included angle between the hypotenuse and the distance between Jack and the base of the building is 67°. From definition:

tan(α) = opposite/adjacent

tan(67) = x/400

x = tan(67)*400

x = 965.7 ft

Then, the height of the building is 965.7 ft - 5 ft = 960.7 ft