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,

$\frac{BC}{sinA}=\frac{AB}{SinC}$

$\frac{BC}{sin(18.6)}= \frac{646}{sin(68.4)}$

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

$BC = \frac{646*sin(18.6)}{sin(68.4)}$

$BC = \frac{646 * 0.3190}{0.9298}$

$BC = 221.63$

$BC = 222$ meters

Therefore, the distance across the river is 222 meters.

Happy to help :)

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