Question

How do you find a missing side of a triangle using SOH CAH TOA

Answer 1

See explanation and attachment

Explanation:

SOH CAH TOA is a mnemonic.

SOH means
`\sin \theta=(Opposite)/(Hypotenuse)`

CAH means
`\cos \theta =(Opposite)/(Hypotenuse)`

TOA means
`\tan \theta=(Opposite)/(Adjacent)`

Given an angle and a side of a right angle triangle, you can use the appropriate ratio to find the missing side.

For instance, find x in the diagram in the attachment.

In this case the best ratio to use is TOA.

`\tan 60\degree=(√(3) )/(x)`

`\implies x=(√(3) )/(\tan 60)`

`x=(√(3) )/(√(3) ) =1`

All the other ratio also follow the same pattern

NB: Your calculator in degree should give
`\tan 60\degree=√(3)`