A museum patron whose eye level is 4 feet above the floor is studying a painting that is 8 feet in height and mounted on the wall 4 feet above the floor. If the patron is x feet from the wall, $\theta$ is the angle that the patron's eye sweeps from the top to the bottom of the painting. Find the measure of the angle $\theta$ for x = 20. Round to the nearest degree).
A) 22°
B) 0.4°
C) 68°
D) 11°

Question

Quizplus · Accepted Answer

The angle can be found using trigonometry, specifically the tangent function, which relates an angle of a right triangle to the ratio of the opposite side over the adjacent side. Here, the opposite sides are the distances from the eye level to the top and bottom of the painting (4 feet to the top and 12 feet to the bottom), and the adjacent side is the distance from the wall (20 feet). Calculating the angles to the top and bottom of the painting and subtracting gives the total angle swept by the eye. The calculations yield an angle of approximately 22 degrees.

A Museum Patron Whose Eye Level Is 4 Feet Above θ\thetaθ

A Museum Patron Whose Eye Level Is 4 Feet Above $\theta$