Question

right triangle trigonometry - sohcahtoa
right triangle trigonometry relates the sides of a right triangle to the angle measures of the two acute angles.
calculate the value for x.
answer (round to nearest degree): x = □°

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, for an acute angle \(x\), \(\sin x=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the side opposite to angle \(x\) is \(2\) and the hypotenuse is \(3\). So, \(\sin x=\frac{2}{3}\).

Step2: Solve for \(x\)

We know that \(x = \sin^{-1}(\frac{2}{3})\). Using a calculator, \(x=\sin^{-1}(\frac{2}{3})\approx41.81^{\circ}\).

Step3: Round to the nearest degree

Rounding \(41.81^{\circ}\) to the nearest degree gives \(42^{\circ}\).

Answer:

$42$