Question

In photography, the angle formed by the top of the subject, the camera, and bottom of the subject is called the viewing angle, as shown at the right. Natalie is taking a picture of Bigfoot #5 which is 15 feet 6 inches tall. She sets her camera on a tripod that is 5 feet above ground level. The vertical viewing angle of her camera is set for 90°.

How far away from the truck should Natalie stand so that she perfectly frames the entire height of the truck in her shot?

Answer 1

Let x be the distance from the truck where Natalie should stand so that she perfectly frames the entire height of the truck in her shot.

Let ∠ACB = θ, then ∠CAD = θ and ∠EAD = 90° - θ

tan θ = opposite side / adjacent side

tan (90° - θ) = cot θ

In △ ABC, tan θ = AB / BC = 60 / x

In △ EDA, tan (90° - θ) = cot θ = ED / AD = 126 / x

cot θ = 1 / tan θ

So, tan θ = x / 126

Equating the expressions for tan θ,

60 / x = x / 126

x^2 = 126 * 60 = 7560

x = 86.95 inches

Natalie should stand 86.95 inches or 7.25 ft from the truck.