In a 45^(∘)-45^(∘)-90^(∘) triangle the hypotenuse is always sqrt(2) times longer than any of the legs, so we can determine the length of the hypotenuse.
Hypotenuse: legsqrt(2)= sqrt(2)sqrt(2)=2
Now we have all the information we need to determine the perimeter and area of the triangle.
b Since this is a right triangle with a second known angle of 60^(∘), we know that this is a 30^(∘)-60^(∘)-90^(∘) triangle. In such a triangle, if the shorter leg is a units then the second leg is sqrt(3)a units and the hypotenuse is 2a units.
In the given triangle, the hypotenuse is 10 feet. By equating this measure with 2a we can find the measure of a, which allows us to calculate the unknown legs.
