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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

Best Answer 

 #1
avatar+6959 
+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

 

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

hectictar  Apr 3, 2018
edited by hectictar  Apr 3, 2018
Sort: 

1+0 Answers

 #1
avatar+6959 
+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

 

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

hectictar  Apr 3, 2018
edited by hectictar  Apr 3, 2018

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