Question

1. a flag pole 18 feet tall casts a shadow 12 feet long at a specific time of day. find, to the nearest degree, the angle of elevation of the sun at this time of day. choose: 56° 48° 42° 34°

Explanation:

Step1: Identify the right - triangle relationship

We have a right - triangle where the height of the flag pole is the opposite side ($a = 18$ feet) and the length of the shadow is the adjacent side ($b = 12$ feet) with respect to the angle of elevation of the sun $\theta$. The tangent function is used in right - triangles for opposite and adjacent sides, $\tan\theta=\frac{a}{b}$.

Step2: Calculate the tangent of the angle

Substitute $a = 18$ and $b = 12$ into the tangent formula: $\tan\theta=\frac{18}{12}=\frac{3}{2}=1.5$.

Step3: Find the angle

We know that $\theta=\arctan(1.5)$. Using a calculator, $\theta=\arctan(1.5)\approx56.31^{\circ}$. Rounding to the nearest degree, $\theta\approx56^{\circ}$.

Answer:

$56^{\circ}$