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

Answer 1

See 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#

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Answer 2

Charles Autterson

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

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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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.