Question

Need Help understanding this math.

Each will have vertices A, B and C with a point D lying on the line segment AB.

1. If AC = 15, CB = 20, angle ACB = 90◦ and angle ADC = 90◦ , what is CD?

2. If AC = 15, CB = 20, AB = 25 and CD = 12, what is AD? What is DB?

Answer 1

1. C is the right angle so AB is the hypotenuse and AD is the altitude to the hypotenuse.

The hypotenuse is

`AB=c= √(15^2 + 20^2) = √(5^2(3^2+4^2)) = 25`

The area calculations must match. Let h=CD

`\frac 1 2 a b = \frac 1 2 c h`

`h = (ab)/(c) = (15)(20)/25 = 12`

Answer: 12

2. This is the same triangle as above. We seek x=AD and DB=25-x

`12^2 + x^2 = 15^2`

`x = √(3^2(5^2-4^2)) = 9`

AD=9 and DB=25-9=16

Answer: AD=9, DB=16