# Trigonometry and Surds

• Sep 6th 2010, 11:12 AM
OJW
Trigonometry and Surds
Hello there,

I have a problem solving question which has been frustrating me:

A triangle has sides of lengths √6, 3√2 and 3√3 units.

Is the triangle right angled? You must give a reason for your answer.

Any help would be greatly appreciated, thank you.

OJW
• Sep 6th 2010, 11:17 AM
e^(i*pi)
Quote:

Originally Posted by OJW
Hello there,

I have a problem solving question which has been frustrating me:

A triangle has sides of lengths √6, 3√2 and 3√3 units.

Is the triangle right angled? You must give a reason for your answer.

Any help would be greatly appreciated, thank you.

OJW

1) Use Pythagoras Theorem - if the sum of the squares of the two shorter sides equals the square of the longest side then it is a right angled triangle. (in other words does $\displaystyle a^2+b^2=c^2$)

2) Use the cos rule to find an angle - if it's 90 degrees then it's a right angled triangle $\displaystyle \left( \cos(C) = \frac{a^2+b^2-c^2}{2ab}\right)$
• Sep 6th 2010, 11:36 AM
OJW
Quote:

Originally Posted by e^(i*pi)
1) Use Pythagoras Theorem - if the sum of the squares of the two shorter sides equals the square of the longest side then it is a right angled triangle. (in other words does $\displaystyle a^2+b^2=c^2$)

2) Use the cos rule to find an angle - if it's 90 degrees then it's a right angled triangle $\displaystyle \left( \cos(C) = \frac{a^2+b^2-c^2}{2ab}\right)$

Thank you very much, that's a perfect explanation!

OJW