Question

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

the sides are in the ratio 1 : 1 : sqrt2    where sqrt 2 = hypotenuse

so if the length of one of the legs is 2 cm the hypotenuse will be of length 2 *sqrt 2 cms.

b )  sin 45  = 1 / sqrt2  = sqrt2 / 2

c)  if the 2 legs of triangle are both 2 cms area  will be 1/2* 2* 2