Question

a portion of a city map is shown in the figure at the right. if you walk along maple street between 2nd street and elm grove lane, how far do you walk? maple street is about \\(\square\\) yd long between 2nd street and elm grove lane. (do not round until the final answer. then round to the nearest tenth as needed.)

Explanation:

Step1: Identify triangle angles

First, find the third angle of the triangle:
$180^\circ - 47^\circ - 54^\circ = 79^\circ$

Step2: Apply Law of Sines

Let $x$ = length of Maple Street. Use $\frac{x}{\sin 54^\circ} = \frac{214}{\sin 79^\circ}$

Step3: Solve for x

Rearrange to isolate $x$:
$x = \frac{214 \times \sin 54^\circ}{\sin 79^\circ}$
Calculate values: $\sin 54^\circ \approx 0.8090$, $\sin 79^\circ \approx 0.9816$
$x \approx \frac{214 \times 0.8090}{0.9816} \approx \frac{173.126}{0.9816} \approx 176.4$

Answer:

176.4 yd