Find the exact value of side x.

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Expert Answers
baxthum8 eNotes educator| Certified Educator

This is a 30˚-60˚-90˚ triangle.  This has special properties in which the sides have a ratio of `1:sqrt(3):2.`

This means that the side opposite the 60˚ angle is `sqrt(3)`  times larger than the side opposite the 30˚ angle, and the hypotenuse is twice as long as the short side, oppositite the 30˚ angle.

Since, x is opposite the 60˚ angle, x is the long leg, which is `sqrt(3)`  times as long as the short leg, y.

However, y is `1/2` as long as the hypotenuse.  This means y is 5, which is the short leg.  x, the long leg is `sqrt(3)`  times the short leg of 5.

This means x is `5sqrt(3).`

The value of x is `5sqrt(3).`