Question

LAST QUESTION HELP! 90 points!

Use the information to find the length of segment CA.

Image not drawn to scale.

Answer 1

CA = 34.

Explanation:

Given:

ΔBDC and ΔADC are right-angled triangles

In ΔBDC with respect to ∡B

Base = BD = 12

Hypotenuse =BC= 20

Perpendicular = CD

Let's find the length of CD by using Pythagoras' theorem

We have:

`\boxed{ \tt Hypotenuse^2=Base^2+Perpendicular^2}`

`\tt BC^2=BD^2+CD^2`

substituting value

`\tt 20^2=12^2+CD^2`

`\tt CD^2=20^2-12^2`

`\tt CD^2=256`

`\tt CD=√(256)`

`\tt CD=16`

`\hrulefill`

Again,

In ΔADC with respect to ∡A

Base = AD= 30

Hypotenuse =AC

Perpendicular =CD=16

Let's find the length of AC which is hypotenuse by using Pythagoras' theorem

We have:

`\boxed{ \tt Hypotenuse^2=Base^2+Perpendicular^2}`

`\tt AC^2=AD^2+CD^2`

substituting value

`\tt AC^2=30^2+16^2`

`\tt AC^2=1156`

`\tt AC=√(1156)`

`\tt AC \: or \:CA=34`

Therefore, the length of segment CA is 34.