Question

Apply the Pythagorean Theorem to find the value of each missing variable. Express your answer in simplest radical form.

Answer 1

hello to solve this question, we can take the two triangles apart and then solve the individual missing part

let's solve for triangle a

to solve for x, let's use pythagorean theorem

`\begin{gathered} x^2=9^2+5^2 \\ x^2=81+25 \\ x^2=106 \\ \text{take the square root of both sides} \\ x=\sqrt[]{106} \\ x=10.295\approx10.3 \end{gathered}`

let's solve for right-angle triangle b

`\begin{gathered} y^2=5^2+3^2^{} \\ y^2=25+9 \\ y^2=34 \\ \text{take the squre root of both sides} \\ y=\sqrt[]{34} \\ y=5.83 \end{gathered}`

from the calculation above, the value of x and y is 10.30 and 5.83 respectively