The world's tallest unsupported flagpole is a 282-ft steel pole in Surrey, British Columbia. The shortest shadow by the pole during the year is 137 ft long. To the nearest degree what is the angle of elevation of the sun when casting the flagpole's shortest shadow?
We can use trigonometry to solve this problem. Let's denote the height of the flagpole as "h" and the length of the shadow as "s".
From the problem, we know that:
h = 282 ft
s = 137 ft
Let's denote the angle of elevation of the sun as "θ".
We can use the tangent function to find θ:
tan(θ) = opposite/adjacent = h/s
Rearranging this equation, we get:
θ = tan⁻¹(h/s)
Plugging in the values we know, we get:
θ = tan⁻¹(282/137) ≈ 64.5 degrees
Therefore, to the nearest degree, the angle of elevation of the sun when casting the flagpole's shortest shadow is 65 degrees.