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!

Guest Apr 3, 2018

#1**+3 **

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}

x^{2} + x^{2} = 10^{2}

x^{2} + x^{2} = 100

Combine like terms.

2x^{2} = 100

Divide both sides by 2 .

x^{2} = 50

Take the positive square root of both sides.

x = √50

Simplify the radical.

x = √[5 * 5 * 2]

x = 5√2

hectictar Apr 3, 2018

#1**+3 **

Best Answer

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}

x^{2} + x^{2} = 10^{2}

x^{2} + x^{2} = 100

Combine like terms.

2x^{2} = 100

Divide both sides by 2 .

x^{2} = 50

Take the positive square root of both sides.

x = √50

Simplify the radical.

x = √[5 * 5 * 2]

x = 5√2

hectictar Apr 3, 2018