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.

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.

`(\sin 34^o)/(BC)=(\sin 116^o)/(45)\\\\BC=(\sin 34^o* 45)/(\sin 116^o)\\\\BC=28units`

Similarly,

`(\sin 30^o)/(AC)=(\sin 116^o)/(45)\\\\AC=(\sin 30^o* 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.