Question

using trig to find a side
question
solve for $x$. round to the nearest tenth, if necessary.
answer
attempt 1 out of 3
$x = $

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, for angle \(M = 31^{\circ}\), the hypotenuse \(MK = 96\), and we want to find the side \(x=ML\) (adjacent side to angle \(M\)). The cosine ratio is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos M=\frac{ML}{MK}\).

Step2: Substitute the values

Substitute \(M = 31^{\circ}\) and \(MK = 96\) into the cosine formula. We get \(\cos(31^{\circ})=\frac{x}{96}\).

Step3: Solve for \(x\)

Multiply both sides of the equation by \(96\): \(x = 96\times\cos(31^{\circ})\).
We know that \(\cos(31^{\circ})\approx0.8572\). Then \(x=96\times0.8572 = 82.3\) (rounded to the nearest tenth).

Answer:

\(x = 82.3\)