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jekas [21]
3 years ago
14

Solve each triangle. Round your answers to the nearest tenth.​

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

<u>Answer:</u> The value of \angle B is 30^o, the length of BC and AC is 28 units and 25 units respectively.

<u>Step-by-step explanation:</u>

To calculate the value of each part of the triangle, we use:

1) Angle sum property

2) Law of sines

<u>Starting with 1:</u>

Calculating \angle B by angle sum property:

\angle A+\angle B+\angle C=180^o\\\\34^o+\angle B+116^o=180^o\\\\\angle B=(180^o-116^o-34^o)=30^o

<u>Applying 2:</u>

The Law of sines relates the length of the side with the sines of the angle opposite to it.

\frac{\sin 34^o}{BC}=\frac{\sin 116^o}{45}\\\\BC=\frac{\sin 34^o\times 45}{\sin 116^o}\\\\BC=28units

Similarly,

\frac{\sin 30^o}{AC}=\frac{\sin 116^o}{45}\\\\AC=\frac{\sin 30^o\times 45}{\sin 116^o}\\\\AC=25units

Hence, the value of \angle B is 30^o, the length of BC and AC is 28 units and 25 units respectively.

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