Question

Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.

Answer 1

`x =5\sqrt 3`

Explanation:

Given

See attachment for triangle

Required

Find x

To do this, we make use of Pythagoras theorem

`x^2 + 5^2 = 10^2`

Solve the exponents

`x^2 + 25 = 100`

Collect like terms

`x^2 =- 25 + 100`

`x^2 =75`

Take square roots

`x =\sqrt{75`

Expand

`x =\sqrt{25*3`

Split

`x =√(25)*\sqrt 3`

`x =5\sqrt 3`