Question

To find the distance across the river, the given diagram is laid out. what is the distance rounded to the nearest meter?

Answer 1

Given:

Angle A = 18.6°

Angle B = 93°

Length of side AB = 646 meters

To find:

the distance across the river, distance between BC

Steps:

Since we know the measure of 2 angles of a triangle we can find the measure of the third angle.

18.6° + 93° + ∠C = 180°

111.6° + ∠C = 180°

∠C = 180° - 111.6°

∠C = 68.4°

Therefore the measure of angle C is 68.4°.

now we can use the law of Sines,

`(BC)/(sinA)=(AB)/(SinC)`

`(BC)/(sin(18.6))= (646)/(sin(68.4))`

`BC[sin(68.4)] = 646 [sin(18.6)]`

`BC = (646*sin(18.6))/(sin(68.4))`

`BC = (646 * 0.3190)/(0.9298)`

`BC = 221.63`

`BC = 222` meters

Therefore, the distance across the river is 222 meters.

Happy to help :)

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