# How do you solve the triangle ABC given a=7, b=3, c=9?

Feb 25, 2018

As detailed below.

#### Explanation:

Steps 1 : Find the area of the triangle, having known three sides,

using formula ${A}_{t} = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$ where is the semi

perimeter of the triangle.$s = \frac{a + b + c}{2}$

Step 2 : with ${A}_{t}$ known, Find one of the angles $\hat{A}$ using area formula for two sides and the included angle

${A}_{t} = \left(\frac{1}{2}\right) b c \sin A$

Step 3 : Apply Law of Ines to find the remaining two angles $\hat{B} , \hat{C}$

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