Question

Find hacks and round to the nearest 10th of a degree

Answer 1

Answer:

$x=64.1$

Explanation:

Step 1. The first step is to find the missing side of the triangle using the Pythagorean theorem:

In this case:

$\begin{gathered} c=16 \\ b=7 \end{gathered}$

and we need to find a.

Substituting c and b into the Pythagorean theorem formula:

$16^2=a^2+7^2$

Solving for a:

$\begin{gathered} 16^2-7^2=a^2 \\ 256-49^{}=a^2 \\ 207=a^2 \\ \downarrow \\ \sqrt[]{207}=a \end{gathered}$

Step 2. The triangle now is:

And to find angle x we use:

$\begin{gathered} \\ \boxed{\sin x=\frac{\text{opposite side}}{hypotenuse}} \end{gathered}$

Substituting the known values:

$\begin{gathered} \sin x=\frac{\sqrt[]{207}}{16} \\ \end{gathered}$

Step 3. Solving for x:

$\begin{gathered} \sin x=\frac{\sqrt[]{207}}{16} \\ \downarrow \\ x=\sin ^{-1}(\frac{\sqrt[]{207}}{16}) \end{gathered}$

Step 4. Solving the operations:

$\begin{gathered} x=\sin ^{-1}(0.899218) \\ \downarrow \\ \\ x=64.05552 \end{gathered}$

Rounding to the nearest tenth (1 decimal):

$x=64.1$

Answer:

$x=64.1$