Question

g)
in a right - triangle, one of the acute angles is 66°, the adjacent side to this angle is 3.5 m, and the hypotenuse is x. we need to find the value of x.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the cosine of an angle is defined as the adjacent side divided by the hypotenuse. Here, the angle is \(66^{\circ}\), the adjacent side to the angle is \(3.5\) m, and the hypotenuse is \(x\). So, \(\cos(66^{\circ})=\frac{3.5}{x}\)

Step2: Solve for \(x\)

We can re - arrange the formula \(\cos(66^{\circ})=\frac{3.5}{x}\) to solve for \(x\). Cross - multiplying gives us \(x=\frac{3.5}{\cos(66^{\circ})}\)

We know that \(\cos(66^{\circ})\approx0.4067\) (using a calculator). Then \(x = \frac{3.5}{0.4067}\approx8.61\)

Answer:

\(x\approx8.61\) m