Question

trigonometry
progress:
the movement of the progress bar may be uneven because questions can be worl
what are the exact values of a and b?
triangle with right angle at c, angle at a is 30°, hypotenuse ab = 7, side ac = b, side bc = a
options:

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

Explanation:

Step1: Identify triangle type

Right triangle with 30° angle, hypotenuse = 7.

Step2: Find side opposite 30° (a)

$a = \frac{1}{2} \times \text{hypotenuse} = \frac{1}{2} \times 7 = \frac{7}{2}$

Step3: Find side adjacent to 30° (b)

$b = \text{hypotenuse} \times \cos(30^\circ) = 7 \times \frac{\sqrt{3}}{2} = \frac{7\sqrt{3}}{2}$

Answer:

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