Question

solve for x. round to the nearest tenth of a degree, if necessary.
triangle image with right angle at k, hypotenuse lj = 87, leg kj = 57, angle at l is x°

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(LJK\), we know the hypotenuse \(LJ = 87\) and the opposite side to angle \(x\) is \(JK=57\). We use the sine ratio. The sine of an angle in a right - triangle is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin x=\frac{JK}{LJ}\).

Step2: Substitute the values

Substitute \(JK = 57\) and \(LJ = 87\) into the sine formula. We get \(\sin x=\frac{57}{87}\). Simplify \(\frac{57}{87}=\frac{19}{29}\approx0.655\).

Step3: Find the angle \(x\)

To find \(x\), we use the inverse sine function. \(x=\sin^{- 1}(0.655)\). Using a calculator, \(x\approx40.9^{\circ}\).

Answer:

\(x\approx40.9^{\circ}\)