- #1

opus

Gold Member

- 701

- 130

## Homework Statement

Solve the triangle with the given information:

A= 40°, B= 20°, a= 100m

## Homework Equations

The Law of Sines

##\frac{sin\left(A\right)}{a}##=##\frac{sin\left(B\right)}{b}##=##\frac{sin\left(C\right)}{c}##

## The Attempt at a Solution

This is a AAS triangle. And since I'm given two angles, I can find the third by subtracting the two given angles from 180°.

$$∠C=180°-40°-20°=120°$$

I now use the Law of Sines to find the unknowns. I start by finding length b.

$$\frac{a}{sin\left(A\right)}=\frac{b}{sin\left(B\right)}$$

$$\frac{100}{sin\left(40°\right)}=\frac{b}{sin\left(20°\right)}$$

$$b≈53.209$$

Next I'll solve for length c, again using the Law of Sines.

$$\frac{c}{sin\left(C\right)}=\frac{b}{sin\left(B\right)}$$

$$\frac{c}{sin\left(120°\right)}=\frac{53.209}{sin\left(20°\right)}$$

$$c≈134.730$$

Solution:

∠A= 40°

∠B= 20°

∠C= 120°

a= 100 m

b≈ 53.209 m

c≈ 134.730 m

I think I did this correctly. But I don't know how to check this to see if my solution is correct. In a right triangle, I would add the angles up to see if they're equal to 180°, and use Pythagorean's Theorem to check the legs. However in this case, it's an oblique triangle and I can't use Pythagoeran's Theorem. So how can I check this?