Question

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

Answer 1

Answer:

$\frac{10 \sqrt{3} }{3} = b$

Step-by-step 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 $\frac{b}{2}$, while the leg that is opposite from the angle that is 60° is $\frac{b\sqrt{3} }{2}$

In this case, we're given that the side opposite from the 60 degree angle is 5, meaning that 5 is equal to $\frac{b\sqrt{3} }{2}$  

So we can set 5 equal to $\frac{b\sqrt{3} }{2}$, to solve for b:

5=$\frac{a\sqrt{3} }{2}$

Multiply both sides by 2

5*2=b√3

10=b√3

Now divide both sides by √3

$\frac{10}{\sqrt{3} } =b$

rationalize the denominator

$\frac{10 * \sqrt{3} }{\sqrt{3} *\sqrt{3} }$ = b

$\frac{10 \sqrt{3} }{\sqrt{9}}$= b

$\frac{10 \sqrt{3} }{3} = b$

The answer can be left as that.

Hope this helps!