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grin007 [14]
3 years ago
13

Calculate the side lengths a and b to two decimal places.

Mathematics
1 answer:
Zinaida [17]3 years ago
6 0

Answer:

a=10.92 units

b=14.51 units

Step-by-step explanation:

We are given that c=6 units

\angle A=43^{\circ}

\angle B=115^{\circ}

We have to find the side length a and b.

We know that sum of angles of a triangle =180 degrees

\angle A+\angle B+\angle C=180

Substitute the values then we get

43+115+\angle C=180

158+\angle C=180

\angle C=180-158=22^{\circ}

sine law: \frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}

\frac{a}{sin 43^{\circ}}=\frac{6}{sin 22^{\circ}}

a=\frac{6}{sin 22^{\circ}}\times sin 43^{\circ}

a=10.92 units

\frac{b}{sin 115^{\circ}}=\frac{6}{sin 22^{\circ}}

b=\frac{6}{sin 22^{\circ}}\times sin 115^{\circ}=14.51

b=14.51 units

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