Question

the movement of the progress bar may be uneven because questions can be worth more or less (includir
what are the exact values of $a$ and $b$?
$\bigcirc$ $a = 5, b = 5\sqrt{2}$
$\bigcirc$ $a = 5, b = 10\sqrt{3}$
$\bigcirc$ $a = 5\sqrt{3}, b = 5$
$\bigcirc$ $a = 5, b = 5\sqrt{3}$

Explanation:

Step1: Identify side a (opposite 30°)

In a 30-60-90 triangle, the side opposite the 30° angle is half the hypotenuse.
$a = \frac{1}{2} \times 10 = 5$

Step2: Calculate side b (adjacent to 30°)

Use the Pythagorean theorem: $b = \sqrt{10^2 - a^2}$
$b = \sqrt{100 - 25} = \sqrt{75} = 5\sqrt{3}$

Answer:

$a = 5, b = 5\sqrt{3}$ (the fourth option)