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

2 Answers
Psykolord1989 .
Oct 24, 2017

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)/csinAa=sinBb=sinCc.

In our case, this means that sin(145)/33 = sin(B)/7 -> sin B = 7 sin(145)/33 approx 0.121sin(145)33=sin(B)7→sinB=7sin(145)33≈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

sankarankalyanam
Feb 25, 2018

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

Explanation:

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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

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