A photographer is taking pictures of a 150fttall roller coas

A photographer is taking pictures of a 150-ft-tall roller coaster. She sets her camera up on a tripod so that the lens of the camera is 3 ft above ground and takes two pictures. The first picture is taken from 300 feet away with the lens aimed at the top of the roller coaster. The second picture is taken from 200 feet away with the lens aimed two-thirds of the way to the top of the roller coaster (from the ground). Find the two angles at which her camera is aimed for the two different pictures. For which picture is her camera aimed at a steeper angle?

Solution

first picture he takes of the top of roller coster ride and distance between base of roller coster and base of tripod is 300 feet

let the lens makes an angle theta with the top of roller coaster

so applying tan theta formula

tan theta = (150 - 3 )/ 300

tan theta = .49

theta = tan^-1 (.49) = 26.10 degrees

now the photographer is standing 200 feet from the base of roller coaster

lets say it makes an angle of phi

applying tan rule

tan phi = ( 100 - 3 ) / 200

phi = 25.87 degrees

2nd angle is the steeper angle 25.87 degrees