TO FIND X
Given that the triangle is a right-angled triangle, the length of the three sides can be related using the Pythagorean Theorem, given to be:
[tex]c^2=a^2+b^2[/tex]
where c is the hypotenuse, and a and b are the other two sides.
From the diagram provided, we have the following parameters:
[tex]\begin{gathered} a=5 \\ b=x \\ c=12 \end{gathered}[/tex]
Therefore, we can calculate the value of x by substituting the values into the formula above and solving:
[tex]\begin{gathered} 12^2=5^2+x^2^{} \\ 144=25+x^2 \\ x^2=144-25 \\ x^2=119 \\ x=\sqrt[]{119} \\ x=10.91 \end{gathered}[/tex]
The measure of x is 10.91.
TO FIND θ
We can use the Cosine Trigonometric Ratio to calculate the measure of θ, given to be:
[tex]\cos \theta=\frac{\text{adj}}{\text{hyp}}[/tex]
From the diagram provided, we have:
[tex]\begin{gathered} hyp=12 \\ adj=5 \end{gathered}[/tex]
Therefore, we have:
[tex]\begin{gathered} \cos \theta=\frac{5}{12} \\ \theta=\cos ^{-1}(\frac{5}{12}) \\ \theta=65.38\degree \end{gathered}[/tex]
The measure of θ is 65.38°.
