Question

What is the value of x?

O 103
10
10
X
O 513
o 5
60°
2
3
4
5
6
7
8
9
10 11

Answer 1

`5√(3)`

Explanation:

A triangle with angles of 30-60-90 will always have sides that measure in the following proportions:

The side opposite the 30* angle = a

The side opposite the 60* angle =
`a√(3)`

The side opposite the 90* angle = 2a

(I used "a" here because your question uses "x" and I don't want to confuse things, but usually people use "x" rather than "a")

They gave us that the hypotenuse (the side opposite the 90* angle) is 10, from there we can figure out the other sides:

Since the side opposite 90* is 2a, and 2a = 10, divide 10 by 2 and you get a = 5.

Once we know what "a" is, we can fill in the rest:

30* = 5

60* =
`5√(3)`

90* = 10