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, \(\theta = 28^{\circ}\), the hypotenuse \(c = 12\), and the adjacent side is \(x\). So, \(\cos28^{\circ}=\frac{x}{12}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\cos28^{\circ}=\frac{x}{12}\) by \(12\). We get \(x = 12\times\cos28^{\circ}\).
Since \(\cos28^{\circ}\approx0.88295\), then \(x=12\times0.88295 = 10.5954\).

Answer:

\(10.60\)