Answer:
Height of Flagpole: 24.03 feet
Length between tip of flagpole and tip of shadow: 46.67 feet
Step-by-step explanation:
So the angle of elevation (31°) is facing directly opposite of the flagpole. The shadow of the flagpole (40 ft) is adjacent to the angle of elevation. Therefore, the tangent function incorporates both the opposite and adjacent sides of the right triangle created. We would then make the equation and solve for the height of the flagpole which is the opposite side (h in this case):
tanθ = opposite/adjacent
tan(31°) = h/40
40tan(31°) = h
24.03442476 = h
h ≈ 24.03
Therefore, the height of the flagpole is about 24.03 ft.
As for your bonus question, the length of the tip of the flagpole to the tip of the shadow would be the hypotenuse of the triangle created, which can easily be found using the Pythagorean Theorem (using exact values):
a² + b² = c²
(40tan(31))² + (40)² = c²
577.6535736 + 1600 = c²
2177.6535736 = c²
46.66533589 = c
c ≈ 46.67
Therefore, the length from the tip of the flagpole to the tip of the shadow is 46.67 ft.
