Question

How do you solve the triangle given m∠C = 145°, b = 7, c = 33?

Answer 1

See explanation

Explanation:

It is unclear what you meant by "solve. Whether you meant to find all Angle measures, all side lengths, or both.

The law of sines states that there is a ratio between the sine of any angle, and the length of the side facing that angle,. In other words:

`(sin A)/a = (sin B)/b = (Sin C)/c`.

In our case, this means that `sin(145)/33 = sin(B)/7 -> sin B = 7 sin(145)/33 approx 0.121`. Looking at a sin chart or using a calculator to take the arcsin of 0.121, we arrive at `angle B.approx 7°`.

Knowing that the sum of angles in any triangle is equal to 180, we determine `angle A = 180 -145 -7 = 28°` . Then we have `sin angleA approx 0.47`, and thus we can find a:

`0.47/a = 0.121/7 -> a = 7(.47)/(.121) approx 27.19`

Answer 2

`color(red)(hat B = 7^@, hat A = 28^@, a = 27`

Explanation:

Applying Law of Sines,

`sin B = ( b * sin C) / c = (7 sin 145) / 33 = 0.1217`

`hat B = sin ^-1 0.1217 = 7^@`

`hat A = 180 - 145 - 7 = 28^@`

`a = (33 sin 28) / sin 145 = 27`