Question

How to find angle when 3 sides are given but only 1 angle?

Answer 1

To find the angles, sine law can be used. The angles B and C are 38.23° and 53.82° respectively.

Explanation:

Use sine law to find the remaining angles

`(sin B)/(b) =(sinA)/(a) \\(sinB)/(16.1) = (sin88)/(26) \\sinB = (16.1sin88)/(26)\\ sinB = 0.6189\\B = Arcsin0.6189`

B = 38.23°

`(sinC)/(c)=(sinA)/(a) \\(sinC)/(21) = (sin88)/(26) \\sinC = (21sin88)/(26)\\sinC= 0.8072\\ C = Arcsin0.8072`

C = 53.82°

The internal angles of a triangle is 180°

We can check if the sum of the three angles.

A + B + C = 180°

88° + 38.23° + 53.82° = 180°

180.05° ≈ 180°

The angles are approximately 180°.

Note that the slight difference is only because of the rounding off of the values.