Question

right triangle trigonometry - sohcahtoa
right triangle trigonometry relates the sides of a right triangle to the angle measures of the two acute angles.
fill in the missing information.
text should be lower case.
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 \(x\), \(\sin x=\frac{\text{opposite}}{\text{hypotenuse}}\). The side opposite to the angle \(x\) is \(47\) and the hypotenuse is \(56\). So, \(\sin x^{\circ}=\frac{47}{56}\).

Step2: Solve for \(x\)

We know that \(x = \sin^{-1}(\frac{47}{56})\). Using a calculator, \(\sin^{-1}(\frac{47}{56})\approx\sin^{-1}(0.8393)\approx57^{\circ}\) (rounded to the nearest degree).

Answer:

$$\sin x^{\circ}=\frac{47}{56}$$
$$x\approx57^{\circ}$$