Answer:
b = 24
Step-by-step explanation:
Concepts
The Pythagorean Theorem states that the sum of the squares of the two other sides on a right triangle is equal to hypotenuse (longest side) squared. It can be represented by the equation [tex]a^2+b^2=c^2[/tex]. We can also use this formula to solve for the other two legs in the right triangle.
Application
In this case, we're asked to find the length of b in the right triangle, given c as 26 and a as 10. Now, we just apply the formula and solve for b.
Solution
Step 1: Set up equation and simplify.
- [tex]10^2+b^2=26^2[/tex]
- [tex]100+b^2=676[/tex]
Step 2: Subtract 100 from both sides.
- [tex]100+b^2-100=676-100[/tex]
- [tex]b^2=576[/tex]
Step 3: Take square root of both sides.
- [tex]\sqrt{b^2} =\sqrt{576}[/tex]
- [tex]b=24[/tex]
Therefore, b = 24.
