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

`d = 340.7m`

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

`(A)/(Sin\ A) = (B)/(Sin\ B) =(C)/(Sin\ C)`

In this case:

`(d)/(Sin\ 41.6) = (125)/(Sin\ 14.1)`

Make d the subject

`d = (125 * sin\ 41.6)/(sin 14.1)`

`d = (125 * 0.66392621265)/(0.24361501178)`

`d = (82.9907765812)/(0.24361501178)`

`d = 340.663639629`

`d = 340.7m`

Hence, the base of the lake is approximately 340.7m