Answer:
[tex]\frac{10 \sqrt{3} }{3} = b[/tex]
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 [tex]\frac{b}{2}[/tex], while the leg that is opposite from the angle that is 60° is [tex]\frac{b\sqrt{3} }{2}[/tex]
In this case, we're given that the side opposite from the 60 degree angle is 5, meaning that 5 is equal to [tex]\frac{b\sqrt{3} }{2}[/tex]
So we can set 5 equal to [tex]\frac{b\sqrt{3} }{2}[/tex], to solve for b:
5=[tex]\frac{a\sqrt{3} }{2}[/tex]
Multiply both sides by 2
5*2=b√3
10=b√3
Now divide both sides by √3
[tex]\frac{10}{\sqrt{3} } =b[/tex]
rationalize the denominator
[tex]\frac{10 * \sqrt{3} }{\sqrt{3} *\sqrt{3} }[/tex] = b
[tex]\frac{10 \sqrt{3} }{\sqrt{9}}[/tex]= b
[tex]\frac{10 \sqrt{3} }{3} = b[/tex]
The answer can be left as that.
Hope this helps!
