Question

What is the value of x in the figure below? In this diagram . ABD~ CAD

Answer 1

45/4

Explanation:

Answer 2

Step 1

In the right triangle ABC

Find the cosine angle C

`cos(C)=(AC)/(CB)`

we have

`AC=15\ units\\CB=20\ units`

substitute

`cos(C)=(15)/(20)` -------> equation A

Step 2

In the right triangle ACD

Find the cosine angle C

`cos(C)=(CD)/(AC)`

we have

`CD=x\ units\\AC=15\ units`

substitute

`cos(C)=(x)/(15)` -------> equation B

Step 3

Find the value of x

equate equation A and equation B

`(15)/(20)=(x)/(15) \\ \\x*20= 15^(2) \\ \\ x=(225)/(20)`

Simplify Divide by
`5` both numerator and denominator

`x=(225)/(20)=(45)/(4)\ units`

therefore

the answer is

the value of x is
`(45)/(4)\ units`