Question

11. Use this triangle. a. Find the length of the hypotenuse using the special relationships for a 45 –45 –90 triangle. Explain the relationships. b. Write the exact value for sin 45 as a fraction in simplest form. c. Use the formula for the area of a triangle given SAS to find the area of the triangle. Explain your steps. d. Use a different method to find the area of the triangle. Explain your steps.

Answer 1

Given: A S+pecial right triangle with 45-45-90 angles. Since the two angles are equal and are both 45 degrees, the two sides opposite each angle are also equal. So if one leg is 1 unit, then the other leg is also 1 unit and the hypotenuse can be determined using the Pythagorean Theorem:

c^2 = a^2 + b^2
c^2 = 1^2 + 1^2
c = √2