Question

what are the exact values of a and b? o a = 5√3,b = 5 o a = 5,b = 5√2 o a = 5,b = 10√3 o a = 5,b = 5√3

Explanation:

Step1: Identify the triangle type

It's a 30 - 60 - 90 triangle. In a 30 - 60 - 90 triangle, if the hypotenuse $c = 10$, and the side opposite the 30 - degree angle is $a$ and the side opposite the 60 - degree angle is $b$. The ratio of the sides of a 30 - 60 - 90 triangle is $a:b:c=1:\sqrt{3}:2$.

Step2: Find the value of $a$

Since $c = 10$ and $c = 2x$ (where $x$ is the multiplier), then $x = 5$. The side opposite the 30 - degree angle $a=x = 5$.

Step3: Find the value of $b$

The side opposite the 60 - degree angle $b=\sqrt{3}x$. Substituting $x = 5$, we get $b = 5\sqrt{3}$.

Answer:

$a = 5,b = 5\sqrt{3}$ (corresponding to the last option)