Question

which equation could be used to find ( mangle j ) in ( \triangle jkl )?
( x=cos ^{-1}left(\frac{8.8}{11}
ight) )
( x=cos ^{-1}left(\frac{11}{8.8}
ight) )
( x=sin ^{-1}left(\frac{8.8}{11}
ight) )
( x=sin ^{-1}left(\frac{11}{8.8}
ight) )

Explanation:

Step1: Recall the definition of sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\angle J\), the side opposite to \(\angle J\) is \(KL = 8.8\) and the hypotenuse is \(KJ=11\).

Step2: Apply the inverse sine function

If \(\sin x=\frac{\text{opposite}}{\text{hypotenuse}}\), then \(x = \sin^{-1}(\frac{\text{opposite}}{\text{hypotenuse}})\). Substituting the values of opposite (\(8.8\)) and hypotenuse (\(11\)) into the formula for the inverse sine function, we get \(x=\sin^{-1}(\frac{8.8}{11})\).

Answer:

\(x=\sin^{-1}(\frac{8.8}{11})\) (the third option)