Question

A man stands on his balcony, 130 feet above the ground. He looks at the ground, with his sight line forming an angle of 70° with the building, and sees a bus stop. The function d = 130 sec θ models the distance from the man to any object given his angle of sight θ. How far is the bus stop from the man? Round your answer to the nearest foot.

Answer 1

d = 380 feet

Step-by-step explanation:

Height of man = perpendicular= 130 feet

Angle of depression = ∅ = 70 °

distance to bus stop from man = hypotenuse = d = 130 sec∅

As sec ∅ = 1 / cos∅

so d = 130 sec∅ or d = 130 / cos∅

d = 130 / cos(70°)

d = 380 feet