Question

Can somebody explain in great detail how to find a and b??

Answer 1

There is a 45 degree angle and a 90 degree angle in the triangle. The other angle must be 45 degrees. Therefore a = 4.
Using the Pythagorean theorem, (a^2 + b^2 = c^2) we can find b. In this case b is the hypotenuse, so the equation would be 4^2+4^2=b^2. 16 + 16 = b^2.
b^2 = 32. All I did there was simplify. b would = 4√2 which is the same as 5.65685424
Hope this helps :)

Answer 2

So you know that this triangle must be a 45-45-90 degree triangle (you can tell this from the picture!)

The side that is length 4 is opposite from the 45 degree angle, and remember that congruent angles also give you congruent sides. This means that the length of a must be equal to the length of 4, because both are located opposite a 45 degree angle.

To find b, you must know that the hypotenuse of a 45-45-90 triangle is just equal to a
`√(2)`. Thus, the length of b= 4 rt. 2