Question

Will mark brainliest!!!!
In ΔABC, ∠A measures 132° and the values of b and a are 36 and 70, respectively. Find the remaining measurements of the triangle, and round your answers to the nearest tenth. **
∠B = 82.2°, ∠C = 62.8°, c = 40.6
∠B = 82.2°, ∠C = 62.8°, c = 30
∠B = 22.5°, ∠C = 25.5°, c = 40.6
∠B = 22.5°, ∠C = 25.5°, c = 30

Answer 1

Answer:

∠B = 22.5°, ∠C = 25.5°, c = 40.6

Step-by-step explanation:

an angle and 2 sides are given. It just so happens that the angle is across from one of the sides. Using the Law of Sines to find the missing angle B first.

$\frac{sin(132)}{70} =\frac{sinB}{36}$

36 sin(132) = 70 sinB and

$\frac{36sin(132)}{70} =sinB$ and

sinB=0.3821887674

B=$sin^-^1$(0.3821887674)

B = 22.5

Now, find C using the Triangle Angle-Sum Theorem .

C = 180 - 132 - 22.5

C = 25.5 degrees

Using the Law of Sines again with angle A and side A and angle C:

$\frac{sin(132)}{70} =\frac{sin(25.5)}{c}$and

$c=\frac{70sin(25.5)}{sin(132)}$

c=40.6

It is the third option there. Locate the third B and that's where you solution starts.