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 \(X\), the sine ratio is defined as \(\sin X=\frac{\text{opposite}}{\text{hypotenuse}}\). The side opposite to angle \(X\) is \(20\) and the hypotenuse is \(27\). So, \(\sin X=\frac{20}{27}\).

Step2: Calculate the angle \(X\)

We know that if \(\sin X = a\), then \(X=\sin^{- 1}(a)\). Here \(a = \frac{20}{27}\approx0.7407\). Using a calculator, \(X=\sin^{-1}(0.7407)\approx48^{\circ}\) (rounded to the nearest degree).

Answer:

$$ \sin X=\frac{20}{27}, X\approx48^{\circ} $$