the town park does an outdoor movie night every Saturday during the summer on a large screen. Kate is sitting 36 ft from the base of the screen, watching a movie with her family. If the angle of elevation from Kate to the top of the screen is 24 degrees, how tall is the movie screen?
+23252 There is a right triangle formed from Kate, along the ground to the base of the screen, a right angle that the ground forms with the screen, and up the screen to the top of the screen.
Label the point where Kate sits as A, the point where the ground hits the screen as C, and the point at the top of the screen as B.
From corner A, the side AC is the adjacent side and the side CB is the opposite side. Corner C is a right angle.
The trig formula using adjacent and opposite is tangent.
Tangent = Opposite / Adjacent
Tangent (A) = CB / AC.
tan(24) = CB / 36.
CB = 36 x tan(24) = 36 x 0.4452 = 16 feet
+23252 There is a right triangle formed from Kate, along the ground to the base of the screen, a right angle that the ground forms with the screen, and up the screen to the top of the screen.
Label the point where Kate sits as A, the point where the ground hits the screen as C, and the point at the top of the screen as B.
From corner A, the side AC is the adjacent side and the side CB is the opposite side. Corner C is a right angle.
The trig formula using adjacent and opposite is tangent.
Tangent = Opposite / Adjacent
Tangent (A) = CB / AC.
tan(24) = CB / 36.
CB = 36 x tan(24) = 36 x 0.4452 = 16 feet
