Question

HELP ME IN THIS MATH 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

The height of the building is 942.34 feet

Explanation:

Here we have that;

A right triangle is formed with vertices at the base of the building, Jack's eyes and the top of the building

The hypotenuse of the right triangle is formed by Jack's line of sight and the top of the building

The side opposite to the 67° angle is the height of the building

Since the distance from where Jack is standing to the building base = 400 ft = The adjacent side of the formed right triangle

Therefore, Tan(67) = (Height of the building)/(Jack's distance from the building)

Tan(67) = (Height of the building)/400 ft

∴ The height of the building = 400 ft × Tan(67) = 942.34 ft.

Answer 2

Height of the building ≈ 947.34 ft

Explanation:

Jack eyes are 5 ft above the ground .He is standing 500 ft from the base of a building .His line of sight forms angle with the top of the building at 67°. The height of the building can be computed below.

The illustration forms a right angle triangle. The opposite sight of the triangle is the unknown. The height of the building can be found by using the tangential ratio.

adjacent = 400 ft

angle = 67°

tan 67° = opposite/adjacent

tan 67° = a/400

cross multiply

a = 400 tan 67°

a = 400 × 2.35585236582

a = 942.34094633

Adding 5 ft to the total height of the building will be 5 + 942.34094633 = 947.34094633

Height of the building ≈ 947.34 ft