Question

to find the distance across a lake, a surveyor took the measurements in the figure shown. use these measurements to determine how far it is across the lake.
a = \square yd
(round the answer to the nearest whole number.)

Explanation:

Step1: Identify trigonometric ratio

We use tangent: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$

Step2: Substitute known values

$\theta=48^\circ$, adjacent $=520$, opposite $=a$
$\tan(48^\circ)=\frac{a}{520}$

Step3: Solve for $a$

$a = 520 \times \tan(48^\circ)$
Calculate $\tan(48^\circ)\approx1.1106$, so $a\approx520\times1.1106$

Step4: Compute and round

$a\approx577.512$, round to whole number

Answer:

578 yd