Question

Pls help me!!! I need to find what b is??

Answer 1

`(10 √(3) )/(3) = b`

Explanation:

Hi there!

We are given a right triangle (notice the right angle), one angle with a measure of 30° and another with 60°

We are also given that one of the legs (one of the sides that makes up the right angle) is 5

We want to find what b is

This triangle is a special right triangle, a 30-60-90 triangle

In a 30-60-90 triangle, if the hypotenuse (the side opposite from the right angle) is b, the leg that is opposite from the 30° angle is
`(b)/(2)`, while the leg that is opposite from the angle that is 60° is
`(b√(3) )/(2)`

In this case, we're given that the side opposite from the 60 degree angle is 5, meaning that 5 is equal to
`(b√(3) )/(2)`

So we can set 5 equal to
`(b√(3) )/(2)`, to solve for b:

5=
`(a√(3) )/(2)`

Multiply both sides by 2

5*2=b√3

10=b√3

Now divide both sides by √3

`(10)/(√(3) ) =b`

rationalize the denominator

`(10 * √(3) )/(√(3) *√(3) )` = b

`(10 √(3) )/(√(9))`= b

`(10 √(3) )/(3) = b`

The answer can be left as that.

Hope this helps!