Question

Three locations are marked next to a river. Points B and C are on the same side of the river, and point A is on the other side of the river. To find the distance AB across a river, a distance BC of 241 meters is laid off on one side of the river. It is found that the angle at point B is 108.6° and the angle at point C is 14.9°. Find the distance AB (across the river). Round to the nearest meter.

Answer 1

74.31353

=74 m

Explanation:

given that three locations are marked next to a river. Points B and C are on the same side of the river, and point A is on the other side of the river. To find the distance AB across a river, a distance BC of 241 meters is laid off on one side of the river. It is found that the angle at point B is 108.6° and the angle at point C is 14.9°.

we have information about triangle ABC as side BC =241, Angle B = 108.6 and angle C = 14.9 degrees.

Hence this is an obtuse scalene triangle.

Angle ∠A = 56.5° (III angle)

Using sine formula we get

`(AB)/(sin 14.6) =(BC)/(sin 56.5) \\AB = 74.31353`

So distance AB is 74 metres.