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.
What are the missing segment lengths shown in the image?

Answer 1

By applying Pythagoras theorem, the missing segment lengths of this triangles include:

1. CD = 10√2
2. AC = 10√2
3. BC =  10
4. AB = 10

How to find the missing segment lengths?

Since triangle ACD is a right-angle triangle, we would use Pythagoras theorem to find the missing segment lengths of this triangles as follows:

c² = a² + b² ≡ AD² = CD² + AC²

Next, we would use cos trigonometric ratio to find side CD,

cos45 = adjacent/hypotenuse

cos 45 = CD/20

1/√2 = CD/20

CD = 1/√2 × 20

CD = (20√2)/2

CD = 10√2

For side AC, we have:

AD² = CD² + AC²

AC² = AD² - CD²

AC² = 20² - (10√2)²

AC² = 400 - 100(2)

AC = √200

AC = 10√2

From triangle ABC, we have:

cos45 = BC/10√2

BC = 10√2 × cos45

BC = 10√2 × 1/√2

BC = (10√2)/√2

BC = 10

For side AB, we have:

AB² = (10√2)² - 10²

AB² = 200 - 100

AB² = 100

AB = 10.

Read more on Pythagorean theorem here: https://brainly.com/question/23200848

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