Question

11 solve for x
√5
60°
x
15

Explanation:

Step1: Identify trigonometric ratio

In a right - triangle, we know that \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, the angle \(\theta = 60^{\circ}\), the adjacent side to the \(60^{\circ}\) angle is \(\sqrt{5}\), and the hypotenuse is \(x\).

Step2: Recall the value of \(\cos60^{\circ}\)

We know that \(\cos60^{\circ}=\frac{1}{2}\).

Step3: Set up the equation and solve for \(x\)

Using the cosine ratio formula \(\cos60^{\circ}=\frac{\sqrt{5}}{x}\), and substituting \(\cos60^{\circ}=\frac{1}{2}\), we get \(\frac{1}{2}=\frac{\sqrt{5}}{x}\).
Cross - multiplying gives us \(x\times1 = 2\times\sqrt{5}\), so \(x = 2\sqrt{5}\).

Answer:

\(x = 2\sqrt{5}\)