Question

Given that the area of a triangle ABC is 4.5 m², a=4, b=3, find two possible measures for angle C. Round your answer to the nearest tenth

Answer 1

`C = 48.6`

Explanation:

Given

`Area= 4.5m^2`

`a =4`

`b = 3`

Required

Find angle C

The area of the triangle will be calculated using:

`Area = (1)/(2)ab \sin C`

So, we have:

`4.5= (1)/(2) * 4 * 3 * \sin C`

`4.5= 6 * \sin C`

Divide both sides by 6

`0.75= \sin C`

Take arc sin of both sides

`\sin^(-1)(0.75)= C`

`48.6 = C`

`C = 48.6`