Question

What is the value of x? If your answer is not an integer, leave it in simplest radical form.

Answer 1

`x = 5sqrt(3)`

Explanation:

This is a right triangle. We can use the Pythagorean theorem to solve

`a^2 +b^2 = c^2`

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

`25+x^2 = 100`

Subtract 25 from each side :

`25-25 +x^2 = 100-25`

`x^2 = 75`

Take the square root of each side ;

`sqrt(x^2) = sqrt(75)`

`x = sqrt(3*25)`

Remember :
`sqrt(ab) = sqrt(a)sqrt(b)`

`x = sqrt(5)sqrt(3)`

`x = 5sqrt(3)`

Answer 2

x=
`5√(3)`

Explanation:

cos60°y=5

y=5/cos60°=5/0.5=10

x=sin60°y=
`(√(3) )/(2)`x10=
`5√(3)`