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Marek Szanyi · Answer 1 · 2023-12-19T07:14:06+0000

Answer:

$\begin{gathered} AT=8\sqrt[]{3} \\ AC=8 \\ m<strong>Step-by-step explanation:</strong><p>To find the missing lengths of the triangle, use trigonometric ratios for right triangles, which are represented by the following equations:</p>[tex]\begin{gathered} \sin (\text{angle)=}\frac{\text{ opposite}}{\text{ hypotenuse}}_{} \\ \cos (\text{angle)}=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \tan (\text{angle)}=\frac{\text{ opposite}}{\text{ adjacent}} \end{gathered}$

Then, find the opposite and adjacent side given the 60 degrees angle:

$\begin{gathered} \sin (60)=(AT)/(16) \\ AT=16\cdot\sin (60) \\ AT=8\sqrt[]{3} \\ \\ \cos (60)=(AC)/(16) \\ AC=16\cdot\cos (60) \\ AC=8 \end{gathered}$

Now, since the intern angles of a triangle must add up to 180 degrees, given two of the angles find the missing angle:

[tex]\begin{gathered} m

Fine all the missing side lengths and angle measured of each triangle.-example-1

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