Question

4. Find the value of each variable for the right triangles. Make sure all answers are in reduced radical form. Show your work.

Answer 1

Use Pythagorean's, in figure 1: t^2+12^2=13^2. t=\sqrt(13^2-12^2)=\sqrt(25)=5.
In figure 2: 6^2+9^2=x^2. x=\sqrt(36+81)=\sqrt(117)=3*\sqrt(13).

Answer 2

For this case, the first thing you should keep in mind is the Pythagorean theorem to find the required variables.
Triangle number 1:
t ^ 2 + 12 ^ 2 = 13 ^ 2
From here, we clear the value of t:
t = root (13 ^ 2 - 12 ^ 2)
t = 5
Triangle number 2:
x ^ 2 = 6 ^ 2 + 9 ^ 2
From here, we clear the value of x:
x = root (6 ^ 2 + 9 ^ 2)
x = root (117)
x = root (9 * 13)
x = 3raiz (13)
Answer:
The value of the variables searched is:
t = 5
x = 3raiz (13)