Question

in the given diagram, calculate x correct to 2 decimal places. 18 35° x

Explanation:

Step1: Use cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 35^{\circ}\), the hypotenuse \(c = 18\), and the adjacent side to the angle \(35^{\circ}\) is \(x\). So, \(\cos35^{\circ}=\frac{x}{18}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\cos35^{\circ}=\frac{x}{18}\) by \(18\). We get \(x = 18\times\cos35^{\circ}\).
Since \(\cos35^{\circ}\approx0.8192\), then \(x=18\times0.8192 = 14.7456\).

Answer:

\(14.75\)