Question

The picture below shows the path that Puppy Liz is running. The electrical post is 40 feet tall. Puppy Liz usually starts at the bench and runs until she gets to the fire hydrant, rests, and then she runs back to the bench. How far does Puppy Liz run to get to the fire hydrant? Round your answer to the nearest hundredth of a foot.

Answer 1

Answer:

Puppy Liz runs 34.61 ft.

Step-by-step explanation:

From the figure we can extract two triangles: one with angle 34° and adjacent 40ft, the other with angle 34°+23° and adjacent 40ft.

Let us call the distance from the pole to the fire hydrant $d_1$, and the distance from the pole to the bench $d_2$, then the distance $d$ from the fire hydrant to the bench is

$d=d_2-d_1$

which is the distance the Puppy Liz runs.

Now, from trigonometry we have

$tan(34^o)=\frac{d_1}{40}\\\\\therefore d_1= 40*tan(34^o)\\\\ \boxed{d_1=26.98ft}$

and

$tan(34^o+23^o)=\frac{d_2}{40}$

$d_2=40*tan(34^o+23^o)\\\\\boxed{d_2=61.59}$

Therefore, the distance $d$ Puppy Liz runs is

$d=d_2-d_1$

$d=61.59ft-26.98ft\\\\\boxed{d=34.61ft}$