Question

solve for x. round to the nearest tenth of a degree, if necessary.
answer attempt 1 out of 2

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle $\triangle DEF$ with $\angle E = 90^{\circ}$, we know the hypotenuse $DF = 17$ and the side opposite to $\angle D$ (which is $x^{\circ}$) is $EF=7.6$. 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, $\sin x=\frac{EF}{DF}$.

Step2: Substitute the values

Substitute $EF = 7.6$ and $DF = 17$ into the sine formula. We get $\sin x=\frac{7.6}{17}$.

Step3: Calculate the value of $\sin x$

$\frac{7.6}{17}=0.4470588235$.

Step4: Find the angle $x$

To find $x$, we use the inverse - sine function. So, $x=\sin^{- 1}(0.4470588235)$. Using a calculator, $x\approx26.6^{\circ}$.

Answer:

$26.6$