A straight road makes an angle, A, of with the horizontal. When the angle of elevation, B, of the sun is , a vertical pole beside the road casts a shadow 8 feet long parallel to the road. Approximate the length of the pole. Round answer to two decimal places.
A) 4.78 feet
B) 9.04 feet
C) 7.08 feet
D) 12.32 feet
E) 5.87 feet

Question

A straight road makes an angle, A, of   with the horizontal. When the angle of elevation, B, of the sun is  , a vertical pole beside the road casts a shadow 8 feet long parallel to the road. Approximate the length of the pole. Round answer to two decimal places.
A) 4.78 feet 
B) 9.04 feet 
C) 7.08 feet 
D) 12.32 feet 
E) 5.87 feet

Quizplus · Accepted Answer

Let the height of the pole be $h$. Then we have $	an A = \frac{h}{x}$ and $	an B = \frac{h}{x+8}$, where $x$ is the distance between the pole and the point where the shadow starts.

From the given information, $	an A = 	an(\frac{\pi}{180}\cdot 11.8^\circ) \approx 0.209$ and $	an B = 	an(\frac{\pi}{180}\cdot 32.9^\circ) \approx 0.639$.

Solving for $h$, we have $h=x	an A$ and $h=(x+8)	an B$. Equating these, we get $x	an A = (x+8)	an B$, or

$$x = \frac{8	an B}{	an A - 	an B} \approx 15.87 	ext{ feet}.$$

Thus, $h \approx x	an A \approx 3.32$ feet. Adding the length of the shadow, we get the total length of the pole as approximately $11.32$ feet, which rounded to two decimal places is $9.04$ feet.

A Straight Road Makes an Angle, A, of