Question

what are the exact values of a and b? a right triangle abc with right angle at c, angle at a is 30 degrees, hypotenuse ab is 7, side ac is b, side bc is a. options: 1. $a = \frac{7}{2}, b = 7\sqrt{3}$ 2. $a = \frac{7}{2}, b = \frac{7\sqrt{2}}{2}$ 3. $a = \frac{7}{2}, b = \frac{7\sqrt{3}}{2}$ 4. $a = \frac{7\sqrt{3}}{2}, b = \frac{7}{2}$

Explanation:

Step1: Identify triangle type

Right triangle with 30° angle, hypotenuse=7.

Step2: Find side a (opposite 30°)

Opposite 30° = ½ hypotenuse: $a=\frac{7}{2}$.

Step3: Find side b (adjacent 30°)

Use cosine: $\cos30°=\frac{b}{7}$, so $b=7×\frac{\sqrt{3}}{2}=\frac{7\sqrt{3}}{2}$.

Answer:

C. $a = \frac{7}{2}, b = \frac{7\sqrt{3}}{2}$