Question

question
find the length of side ( x ) to the nearest tenth.
answer attempt 1 out of 2
( x = )

Explanation:

Step1: Identify triangle type and trigonometric ratio

This is a right - triangle with angles \(30^{\circ}\), \(60^{\circ}\) and \(90^{\circ}\). We know one leg (length = 5) and we want to find the hypotenuse \(x\). We can use the cosine function. The cosine of an angle in a right - triangle is defined as \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\). For the \(30^{\circ}\) angle, the adjacent side is 5 and the hypotenuse is \(x\). So \(\cos(30^{\circ})=\frac{5}{x}\).

Step2: Solve for \(x\)

We know that \(\cos(30^{\circ})=\frac{\sqrt{3}}{2}\approx0.866\). From \(\cos(30^{\circ})=\frac{5}{x}\), we can re - arrange the formula to solve for \(x\): \(x = \frac{5}{\cos(30^{\circ})}\). Substitute \(\cos(30^{\circ})\approx0.866\) into the formula: \(x=\frac{5}{0.866}\approx5.8\).

Answer:

\(5.8\)