Question

Please help me find the sides of this triangle using the special right triangle method, 45-45-90. With work :)

Answer 1

see explanation

Explanation:

The sides of a 45- 45- 90 triangle are in the ratio 1 : 1 :
`√(2)`

where 1 , 1 are the legs and
`√(2)` the hypotenuse

If we let the ratio be a : a :
`√(2)` a , then

AT = AD = a = 10

DT =
`√(2)` a = 10
`√(2)`

Answer 2

Explanation:

The basic 45-45-90 triangle ratio is :

Side opposite to 45° angle: x

Side opposite to 45° angle: x

Side opposite to 90° angle: x√2

Ratios of sides of 45-45-90 triangle is x : x : x√2

Side opposite to ∠D which is 45° is : 10

AT = x = 10

Side opposite to ∠T which is 45° is : 10

AD = x = 10

Side opposite to ∠A which is 90° is : TD

TD = x√2 = 10*√2 = 10√2