Solve for the remaining angle and sides of the triangle described below. Round to the nearest hundredth:C = 100°, A = 45°, c = 3

Question

asked Aug 25, 2023 31.2k views

1 Answer

John Arlen · Answer 1 · 2023-08-30T01:11:19+0000

step 1

Find out the measure of angle B

Remember that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

A+B+C=180 degrees

substitute given values

45+B+100=180

B=180-145

step 2

Find out the length of the side a

Applying the law of sines

substitute given values

$(a)/(s\imaginaryI n45^o)=(3)/(s\imaginaryI n100^o)$
$a=\frac{3*s\mathrm{i}n45^o}{s\imaginaryI n100^o}$

step 3

Find out the length of the side b

applying the law of sines

$(b)/(s\imaginaryI nB)=(c)/(s\imaginaryI nC)$

substitute given values

$(b)/(s\imaginaryI n35^o)=(3)/(s\imaginaryI n100^o)$
$b=\frac{3*s\mathrm{i}n35^o}{s\imaginaryI n100^o}$