Question

What is the value of x?​

Answer 1

`x = 5\sqrt3`

Explanation:

We can solve for x in this right triangle by using the ratio of the sides in a 30-60-90 triangle:

• 1 : √3 : 2

We can identify the longest side, or hypotenuse (which corresponds to 2 in the ratio), as 10. We can also see that the second largest side (√3 in the ratio) is x.

Therefore, to solve for x, we can multiply 10 by
`(\sqrt3)/(2)` because that is the number which gets 2 to
`\sqrt3`:

`\\ot2 \cdot (\sqrt3)/(\\ot2) = \sqrt3`

`x = 10 \cdot (\sqrt3)/(2)`

`\boxed{x = 5\sqrt3}`