Question

solve for x. round to the nearest tenth of a degree, if necessary.

(right triangle lmn with right angle at m, lm = 3.8, ln = 8, angle at l is x degrees)

answer attempt 1 out of 5
x = °
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Explanation:

Step1: Identify trigonometric ratio

In right triangle \(LMN\) (right - angled at \(M\)), we know the adjacent side to angle \(x\) is \(LM = 3.8\) and the hypotenuse \(LN=8\). The cosine of an angle in a right triangle is defined as \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos(x)=\frac{LM}{LN}=\frac{3.8}{8}\).

Step2: Solve for \(x\)

First, calculate \(\frac{3.8}{8}=0.475\). Then, to find \(x\), we take the inverse cosine (arccos) of \(0.475\). So, \(x = \arccos(0.475)\). Using a calculator, we find that \(x\approx61.6^{\circ}\) (rounded to the nearest tenth of a degree).

Answer:

\(61.6\)