# Solving an oblique triangle. Looking for a correctness check

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## 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?

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kuruman
Homework Helper
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• opus
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We haven't gone over that yet. I will look into that. You're saying I can check these solutions with it?

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After playing around with it a little bit, it looks like my answers were correct (assuming I was using it correctly, but it seems pretty straight forward). Thank you!