Question

in right triangle abc, ∠b is the right angle and m∠c = 30°. if ac = 10, what is ab?
a. 5
b. 5√3
c. 20
d. 5√3/3

Explanation:

Step1: Recall sine - function definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. In right - triangle $ABC$ with $\angle B = 90^{\circ}$, $\angle C=30^{\circ}$, and hypotenuse $AC = 10$, and the side opposite to $\angle C$ is $AB$. So, $\sin C=\frac{AB}{AC}$.

Step2: Substitute the values

We know that $\sin30^{\circ}=\frac{1}{2}$ and $AC = 10$. Substituting into the formula $\sin C=\frac{AB}{AC}$, we get $\frac{1}{2}=\frac{AB}{10}$.

Step3: Solve for $AB$

Cross - multiply the equation $\frac{1}{2}=\frac{AB}{10}$ to get $AB=\frac{1}{2}\times10 = 5$.

Answer:

A. 5