Question

in the given diagram, calculate x correct to 2 decimal places.

Explanation:

Step1: Use cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 26^{\circ}\), the hypotenuse is \(25\) and the adjacent side is \(x\). So, \(\cos(26^{\circ})=\frac{x}{25}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\cos(26^{\circ})=\frac{x}{25}\) by \(25\). We get \(x = 25\times\cos(26^{\circ})\).
We know that \(\cos(26^{\circ})\approx0.8988\). Then \(x=25\times0.8988 = 22.47\).

Answer:

\(22.47\)