Question

select the correct answer.
what is the value of x?
a. 10.6
b. 7.5
c. 21.2
d. 15

Explanation:

Step1: Find the other non - right angle

Since the sum of angles in a triangle is \(180^{\circ}\), and one angle is \(90^{\circ}\) and another is \(45^{\circ}\), the third angle is \(180-(90 + 45)=45^{\circ}\).

Step2: Use the sine rule

The sine rule states that \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). Let the side opposite \(45^{\circ}\) be \(x\) and the side opposite \(90^{\circ}\) be \(15\). So \(\frac{x}{\sin45^{\circ}}=\frac{15}{\sin90^{\circ}}\).
Since \(\sin45^{\circ}=\frac{\sqrt{2}}{2}\approx0.707\) and \(\sin90^{\circ} = 1\), then \(x = 15\times\sin45^{\circ}\approx15\times0.707 = 10.6\).

Answer:

A. 10.6