+1023 When the sun is shining at a 62º angle of elevation, a flagpole forms a shadow of length x feet. Later, the sun shines at an angle of 48º, and the shadow is 16 feet longer than before.
A. Write two expressions for the height h of the flagpole in terms of x.
B. How tall is the flagpole?
+23252 A)
Let h represent the height of the flagpole.
When the angle of elevation is 62°, tan(62°) = h/x ---> x = h/tan(62°)
When the angle of elevation is 48°, tan(48°) = h/(x+16) ---> x + 16 = h/tan(48°) ---> x = h/tan(48°) - 16
B)
Since there are two equations for x, they can be set equal to each other.
h/tan(62°) = h/tan(48°) - 16
h/1.8807 = h/1.1106 - 16 (since 1/1.8807 = 0.5317 and 1/1.1106 = 0.9904) --->
0.5317h = 0.9004h - 16 (subtract 0.9004 from both sides) --->
- 0.4587h = -16 (divide both sides by -0.4587) --->
h = 35 feet (approximately)
