Question

what is the approximate length of side ab in triangle abc?

a. 15.2 units
b. 14.0 units
c. 37.9 units
d. 41.2 units

Explanation:

Step1: Find angle at A

Sum of angles in triangle: $180^\circ - 65^\circ - 35^\circ = 80^\circ$

Step2: Apply Law of Sines

$\frac{AB}{\sin C} = \frac{BC}{\sin A}$ → $AB = \frac{BC \cdot \sin C}{\sin A}$

Step3: Calculate AB

$AB = \frac{24 \cdot \sin 35^\circ}{\sin 80^\circ} ≈ \frac{24 \cdot 0.5736}{0.9848} ≈ 15.2$ units

Answer:

A. 15.2 units