Use the law of sines to find the measure of angle C.

C = 43.6 degrees (1 dp)

You cannot find C using the sine law without knowing one of the other angles.
In your previous question I showed you that A = 71.5
sin(C)/16 = sin(71.5...)/22
sin(C) = 16 x sin(71.5...)/22 = 0.68977...
C = sin^-1(0.68969) = 43.6 degrees

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varshamittal029 varshamittal029 · Answer 2 · 2022-07-08T07:48:24+02:00

Here, if you use the law of sines, you cannot find the measure of the required angle. But if you use the law of cosines, you will get the desired result.

The measure of the angle C of the given triangle is 43.61°

What is the law of cosines?

According to the law of cosine, the square of any one side of a triangle is equal to the difference between the squares of the other two sides and double the product of the other sides and cosine angle added together between them. If AB, BC, and CA are lengths of the three sides of a triangle, then using the law of cosine, we can write

AB² = BC² + CA² - 2(BC)(CA)cos C.

How to solve this problem?

Here, AB = 16, BC = 22, and AC = 21.

Now, 16² = 22² + 21² - 2 * 22 * 21 * cos C

i.e. 256 = 484 + 441 - 924 * cos C

i.e. 256 - 925 = - 924 * cos C

i.e. - 669 = - 924 * cos C

i.e. cos C = 669/924 = 0.724

i.e. C = cos⁻¹(0.724) = 43.61

Therefore the measure of the angle C of the given triangle is 43.61°

Learn more about law of cosines here -

https://brainly.com/question/4472157

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