how to solve the triangle for all angles and sides m<A=60 degree b= 16 cm a= 8 square root 3 cm

Question

I'm trying to help my son and I'm lost....

Answer 1

Hello Tuesday,

 

If the triangle in question is a right triangle, then the angle measurements will be:

 

<A= 60°

<B= 90°

<C= 30°

 

measure of side a= 8√3

measure of side b= 16

 

measure of side c will be figured by using the Pythagorean theorem, a²+b²=c²

 

16² + (8√3)²=c²

256 + (64*3)=c²

256+192=c²

448=c²

√448=c

Next, we need to simplify √448

To do this, we need to find which perfect square (4, 9, 16, 25....) evenly divides into 448

Lets divide 448 by 4:  448÷4=112

Divide by 4 again: 112÷4= 28

Divide by 4 again: 28÷4=7

 

So, we know 4*4*4*7=448

Find the square roots of each term:  2*2*2*√7=√448

Simplify:  8√7=√448

 

So c= 8√7