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 =? 44° 600 yds a = □ yd (round the answer to the nearest whole number.)

Explanation:

Step1: Identify the trigonometric ratio

We have a right - triangle with an angle of $44^{\circ}$, adjacent side $AC = 600$ yds and we want to find the opposite side $a$. We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.
$\tan\theta=\frac{a}{AC}$

Step2: Substitute the values

Given $\theta = 44^{\circ}$ and $AC = 600$ yds, we substitute into the formula: $\tan(44^{\circ})=\frac{a}{600}$.
So, $a = 600\times\tan(44^{\circ})$.

Step3: Calculate the value

We know that $\tan(44^{\circ})\approx0.9657$. Then $a = 600\times0.9657=579.42$.

Step4: Round the answer

Rounding $579.42$ to the nearest whole number, we get $a\approx579$.

Answer:

$579$