Question

select the correct answer.
what is the value of x in the triangle?

a. 15\sqrt{3}
b. 7.5
c. 5
d. 5\sqrt{3}
e. 15

Explanation:

Step1: Use trigonometric ratio

In a right - triangle, we know that \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 30^{\circ}\), the hypotenuse is \(15\), and the side opposite to \(30^{\circ}\) is \(x\).

Step2: Apply the formula

We use the formula \(\sin30^{\circ}=\frac{x}{15}\). Since \(\sin30^{\circ}=\frac{1}{2}\), we have the equation \(\frac{1}{2}=\frac{x}{15}\).

Step3: Solve for \(x\)

Cross - multiply: \(x = 15\times\frac{1}{2}=7.5\)

Answer:

B. \(7.5\)