Question

On a windless day In Janurafy, Carl ties 300 helium filled balloons to his lawn chair 80ft from his 20ft tall house, and begins a vergical ascent into the sky. Hos high is carl when the angle lf depression from carl to the top of his house is 42°

Answer 1

The answer is below

Explanation:

θ = 90° - 42° = 48°

The angle formed is a right angled triangle, therefore trigonometric identities can be used to find the length of the triangle sides.

tan(θ) = opposite / adjacent

tan(48) = 80 / h

h = 80 / tan(48)

h = 72.03 ft

h is the vertical distance from carl to the top of his house, to get his total height to the ground (H), we use:

H = h + height of house

H = 72.03 + 20

H = 92.03 ft

Therefore Carl is 92.03 ft high