# Solve the Triangle tri{}{45}{9}{45}{}{90}

Solve the Triangle tri{}{45}{9}{45}{}{90}
Find .
The cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse.
Substitute the name of each side into the definition of the cosine function.
Set up the equation to solve for the adjacent side, in this case .
Substitute the values of each variable into the formula for cosine.
Combine and .
Find the last side of the triangle using the Pythagorean theorem.
Use the Pythagorean theorem to find the unknown side. In any right triangle, the area of the square whose side is the hypotenuse (the side of a right triangle opposite the right angle) is equal to the sum of areas of the squares whose sides are the two legs (the two sides other than the hypotenuse).
Solve the equation for .
Substitute the actual values into the equation.
Raise to the power of .
Use the power rule to distribute the exponent.
Apply the product rule to .
Apply the product rule to .
Simplify the numerator.
Raise to the power of .
Rewrite as .
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Evaluate the exponent.
Reduce the expression by cancelling the common factors.
Raise to the power of .
Multiply by .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Rewrite as .
Simplify the numerator.
Rewrite as .
Pull terms out from under the radical.
The absolute value is the distance between a number and zero. The distance between and is .
Multiply by .
Combine and simplify the denominator.
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.