Question

Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on land such than

Answer 1

670.5 m

Explanation:

We can use Sine Rule of Triangle, where:

`(a)/(sinA) = (b)/(sinB) = (c)/(sinC)`

Note:

`a = BC`

`b = AC`

`c = AB`

First step, find the value of ∠B by using Sine Rule.

`(a)/(sinA) = (b)/(sinB)`

`(523)/(sin(51.1)) = (385)/(sinB)`

`sinB = 385 \cdot sin(51.1) \cdot (1)/(523)`

`sinB = 0.573`

`B = 35.0`

Second step, find the value of ∠C.

The sum of all angles in triangle is 180°

`A + B + C = 180`

`51.1 + 35.0 + C = 180`

`C = 93.9`

Final step, find the value of AB by using Sine Rule again.

`(a)/(sinA) = (c)/(sinC)\\\\(523)/(sin(51.1)) = (c)/(sin(93.9))\\\\\\c = (523)/(sin(51.1)) \cdot sin(93.9)\\\\c = 670.5`

Now, we get the final answer as, AB = 670.5 m