Question

Drag each length to the correct location on the image. Each length can be used more than once, but not all lengths will be used.

Answer 1

Answer:

The length of the unknown sides of the triangles are as follows:

CD = 10√2

AC = 10√2

BC =  10

AB = 10

ΔACD is a right angle triangle. Therefore, Pythagoras theorem can be used to find the sides of the triangle.

c² = a² + b²

where

c = hypotenuse side = AD = 20

a and b are the other 2 legs

lets use trigonometric ratio to find CD,

cos 45 = adjacent / hypotenuse

cos 45 = CD / 20

CD = 1 / √2 × 20

CD = 20 / √2 = 20√2 / 2 = 10√2

20² - (10√2)² = AC²

400 - 100(2)  = AC²

AC² = 200

AC = √200 = 10√2

ΔABC is a right angle triangle too. Therefore,

AB² + BC² = AC²

Using trigonometric ratio,

cos 45 = BC / 10√2

BC = 10√2 × cos 45

BC = 10√2 × 1 / √2

BC = 10√2 / √2 =  10

(10√2)² - 10² = AB²

200 - 100 = AB²

AB² = 100

AB = 10

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

the first square is 12/\2 and middle square is 24 and the one at the left is 12/\3