Question

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

Answer 1

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

Step-by-step explanation:

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

1) Angle sum property

2) Law of sines

Starting with 1:

Calculating $\angle B$ by angle sum property:

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

Applying 2:

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.