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

Explanation:

Step1: Identify the trigonometric relation

In right - triangle ABC, we know the adjacent side to the angle \(A = 44^{\circ}\) is \(AC = 630\) yds and we want to find the opposite side \(a\). We use the tangent function, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).
\(\tan A=\frac{a}{AC}\)

Step2: Solve for \(a\)

Given \(A = 44^{\circ}\) and \(AC = 630\) yds. We have \(a = AC\times\tan A\). Substitute the values: \(a=630\times\tan(44^{\circ})\).
Since \(\tan(44^{\circ})\approx0.9657\), then \(a = 630\times0.9657\).
\(a=630\times0.9657 = 608.391\)

Step3: Round the answer

Rounding \(608.391\) to the nearest whole number, we get \(a\approx608\) yds.

Answer:

608