Question

angle trigonometry. which equation can be used to find the measure of angle lkj? $sin^{-1}(\frac{10.8}{8.9}) = x$, $cos^{-1}(\frac{10.8}{8.9}) = x$, $cos^{-1}(\frac{8.9}{10.8}) = x$, $sin^{-1}(\frac{8.9}{10.8}) = x$

Explanation:

Step1: Recall trigonometric - ratio definitions

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$ and $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$. Let's assume for angle $\angle LKJ$, the opposite side has length $10.8$ cm and the hypotenuse has length $13.8$ cm.

Step2: Use inverse - sine formula

To find the angle $\theta=\angle LKJ$, we use the inverse - sine function. Since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, then $\theta=\sin^{- 1}(\frac{\text{opposite}}{\text{hypotenuse}})$. Substituting the values, we get $\theta=\sin^{-1}(\frac{10.8}{13.8})$.

Answer:

$\sin^{-1}(\frac{10.8}{13.8})=x$ (the first option in the multiple - choice list)