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?
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.
Get Answers For Free
Most questions answered within 1 hours.