Question

select the correct answer.
what is the approximate length of side ab in triangle abc?
a. 15.2 units
b. 37.9 units
c. 41.2 units
d. 14.0 units

Explanation:

Step1: Find angle A

Sum of angles in a triangle is \(180^{\circ}\). So, \(\angle A=180^{\circ}-65^{\circ}-35^{\circ}=80^{\circ}\)

Step2: Apply the Law of Sines

The Law of Sines states \(\frac{AB}{\sin C}=\frac{BC}{\sin A}\). Given \(BC = 24\), \(\angle C = 35^{\circ}\), \(\angle A=80^{\circ}\). Then \(AB=\frac{24\times\sin35^{\circ}}{\sin80^{\circ}}\)

Step3: Calculate the values

We know that \(\sin35^{\circ}\approx0.5736\) and \(\sin80^{\circ}\approx0.9848\). So, \(AB=\frac{24\times0.5736}{0.9848}\approx14.0\)

Answer:

D. 14.0 units