Question

find x using the right triangle shown. round your answer to the nearest tenth (trigonometric ratios) the right triangle has a right angle, one angle is 28°, one side is 11, the side opposite to 28° is x? (the options are 9.7, 5.8, 5.2, 20.7)

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle with an angle of \(28^\circ\), the side opposite to the angle \(28^\circ\) is \(x\), and the side adjacent to the angle \(28^\circ\) is \(11\). The tangent function relates the opposite and adjacent sides: \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). So \(\tan(28^\circ)=\frac{x}{11}\).

Step2: Solve for \(x\)

Multiply both sides by \(11\) to get \(x = 11\times\tan(28^\circ)\). Calculate \(\tan(28^\circ)\approx0.5317\). Then \(x = 11\times0.5317\approx5.8487\), which rounds to \(5.8\) when rounded to the nearest tenth.

Answer:

\(5.8\)