back to *math video class*

- Use Pythagorean to solve a right triangle problem
- Question:
- ABC is a right triangle with the angle C is 90
^{o}. If the angle B is 30^{o}, what is the length of AC?

- Solution:
- let the length of AC be x, that is, AC = x
- since ABC is a right triangle (Given), the angle B is 30
^{o} witch opposite AC
- since AB is the hypotenuse of the right triangle, and the angle B is 30
^{o} and it opposite AC
- so AB = 2 AC
- since in a right triangle, the side opposite 30
^{o} is one-half the hypotenuse.
- so AB = 2 AC = 2x
- Pythagorean theorem: the square of the hypotenuse is equal to the sum of the square of two legs.
- that is, AB
^{2} = AC^{2} + BC^{2}
- Given: BC = 3 feet
- (2x)
^{2} = x^{2} + 3^{2}
- 4x
^{2} = x^{2} + 9
- move the variable to the left side of the equation
- 4x
^{2} - x^{2} = 9
- 3x
^{2} = 9
- divide by 3 in both side of the equation
- x
^{2} = 3
- since x is the length of AC, so x must be possitive
- so x = square root of 3.
- so the length of AC is square root of 3 feet.