Question

oTo find the distance across a lake, a surveyor took the measurements shown in the figure. Use these measurements to determine how far itis across the lakeB500590 ydСThe distance across the lake is(Round to the nearest whole number as needed.)Enter your answer in the answer box

Answer 1

703 yds

Step-by-step explanation:

To find the distance (i.e. the values of a), apply trigonometrical ratio.

• The side ,opposite ,angle 50 degrees, BC = a

,

• The side ,adjacent to ,angle 50 degrees, AC = 590 yds

`\tan \theta=\frac{\text{Opposite}}{\text{Adjacent}}`

Therefore:

`\begin{gathered} \tan A=(BC)/(AC) \\ \tan 50\degree=(a)/(590) \end{gathered}`

Cross multiply:

`\begin{gathered} a=590*\tan 50\degree \\ a=703.13 \\ a\approx703\text{ yds.} \end{gathered}`

The distance across the lake is 703 yards (to the nearest whole number).