If you could once again show me the steps for this question I would appreciate that a lot! I am almost done with this unit I just have to be sure I don't have to redo it, special thanks to Cphill for being persistant in helping me. Thank you!
Since the sum of the angles in a triangle is 180° and two of the angles are 90° and 45°,
the measure of the third angle = 180° - 90° - 45°
the measure of the third angle = 45°
Since two of the angles in the triangle are 45°, it is an isosceles triange, and the sides opposite the 45° angles have the same length. So the unlabeled side has a length of x .
Now we can use the Pythagorean theorem to find x .
(leg)2 + (other leg)2 = (hypotenuse)2
x2 + x2 = 102
x2 + x2 = 100
Combine like terms.
2x2 = 100
Divide both sides by 2 .
x2 = 50
Take the positive square root of both sides.
x = √50
Simplify the radical.
x = √[5 * 5 * 2]
x = 5√2
Since the sum of the angles in a triangle is 180° and two of the angles are 90° and 45°,
the measure of the third angle = 180° - 90° - 45°
the measure of the third angle = 45°
Since two of the angles in the triangle are 45°, it is an isosceles triange, and the sides opposite the 45° angles have the same length. So the unlabeled side has a length of x .
Now we can use the Pythagorean theorem to find x .
(leg)2 + (other leg)2 = (hypotenuse)2
x2 + x2 = 102
x2 + x2 = 100
Combine like terms.
2x2 = 100
Divide both sides by 2 .
x2 = 50
Take the positive square root of both sides.
x = √50
Simplify the radical.
x = √[5 * 5 * 2]
x = 5√2