Question

A surveyor is trying to find the length of a lake. He finds a baseline distance AB of 125 m. Angle A is measured to be 41.6° and angle B is measured at 124.3°. Find the length of the lake d. Please and Thank you.

Answer 1

Answer:

$d = 340.7m$

Step-by-step explanation:

See attachment for question illustration

From the attachment, we have:

$AB = 125m$

$<A = 41.6$

$<B = 124.3$

Required

Solve d

First, we need to calculate <C

$<A + <B + <C = 180$ --- angles in a triangle

$41.6+ 124.3 + <C = 180$

$165.9+ <C = 180$

Make <C the subject

$<C = 180 - 165.9$

$<C = 14.1$

Next, we apply Sine's law to solve for d

$\frac{A}{Sin\ A} = \frac{B}{Sin\ B} =\frac{C}{Sin\ C}$

In this case:

$\frac{d}{Sin\ 41.6} = \frac{125}{Sin\ 14.1}$

Make d the subject

$d = \frac{125 * sin\ 41.6}{sin 14.1}$

$d = \frac{125 * 0.66392621265}{0.24361501178}$

$d = \frac{82.9907765812}{0.24361501178}$

$d = 340.663639629$

$d = 340.7m$

Hence, the base of the lake is approximately 340.7m