Question

100 POINTS!!! To find the distance AB across a river, a distance BC of 319 m is laid off on one side of the river. It is found that B = 104.6° and C = 14.4°. Find AB.

Answer 1

Answer: AB = 90.7 meter

Given following:

• BC = 319 meter

• angle B = 104.6°

• angle C = 14.4°

Find angle A :

⇒ 180° - (104.6° + 14.4°)

⇒ 61°

Now, use sine rule:

`\sf (AB)/(BC) = (sin(C^(\circ )))/(sin(A^(\circ \:)))`

`\sf (AB)/(319) = \frac{sin(14.4) } {sin(61)}`

`\sf AB = \frac{319 \ sin(14.4) } {sin(61)}`

`\sf AB = 90.70464953 \quad \approx \quad 90.7 \ m \ (rounded \: to \: nearest \ tenth)`