Question

Use the triangle below to find cos V.

Answer 1

`cos\ V = (2√(29))/(29)`

Explanation:

Given

The attached triangle

Required

Find cos V

In trigonometry:

`cos\theta = (Adjacent)/(Hypotenuse)`

In this case:

`cos V= (TV)/(UV)`

Where

`TV = 6`

and

`UV^2 = TV^2 + TU^2` -- Pythagoras

`UV^2 = 6^2 + 15^2`

`UV^2 = 261`

Take square roots

`UV = \sqrt{261`

`UV = \sqrt{9*29`

`UV = √(9) *\sqrt{29`

`UV = 3\sqrt{29`

So:

`cos V= (TV)/(UV)`

`cos\ V = (6)/(3√(29))`

`cos\ V = (2)/(√(29))`

Rationalize:

`cos\ V = (2)/(√(29))*(√(29))/(√(29))`

`cos\ V = (2√(29))/(29)`