Answer: 50.8
We can answer this question by using the Trigonometric Functions sine and cosine.
To find an angle using the sine function, we know that:
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypotenuse} \\ \theta=\sin ^{-1}\frac{opposite}{hypotenuse} \end{gathered}[/tex]
This will give us:
[tex]\theta=\sin ^{-1}\frac{2\sqrt[]{6}}{2\sqrt[]{15}}=39.2\degree[/tex]
Then, to find the other angle, we can either:
- Add 39.2 and 90, then subtract from 180, or
- Use the trigonometric function cosine.
Let us first try using the function cosine:
[tex]\begin{gathered} \cos \theta=\frac{adjacent}{hypotenuse} \\ \theta=\cos ^{-1}\frac{adjacent}{hypotenuse} \end{gathered}[/tex]
This will give us:
[tex]\theta=\cos ^{-1}\frac{2\sqrt[]{6}}{2\sqrt[]{15}}=50.8\degree[/tex]
Then let us try adding 90 and 39.2 then subtract it from 180
[tex]180\degree-(90\degree+39.2\degree)=50.8\degree[/tex]
Now, we have the value of two acute angles which are 39.2 and 50.8. Since we are asked for the larger acute angle, the answer would be 50.8.
