Question

PLSPLSPLSPLS HELP.

In the diagram below, is an altitude of ABD. What is the length of ? If necessary, round your answer to two decimal places.

(Picture below.)

Answer 1

First try to prove triangle ACB and ABD are similar. Similar triangles have proportional sides (meaning sides in the big triangle are a constant factor times the sides in the small one).

Further hint: you may need the Pythagorean Theorem as well...

Answer 2

a^2+b^2=c^2.
Where do I input 16 and 30?

Answer 3

16 = a,
30 = c?

Answer 4

a and b are the rectagular sides, c is the hypothenuse

Answer 5

16^2+b^2=30^2
B= 25.38?

Answer 6

No, a and b are the rectangular sides. In triangle ACB these are 16 and 30, so c²=16²+30²=256+900=1156, so c=34.

Answer 7

So AB=34.

Answer 8

Now what do I do to find CD?

Answer 9

@ZeHanz

Answer 10

ACB and ABD are similar, because they both have a right angle, and they have angle A in common.
Similar triangles have proportional sides, which means:\[\frac{ AC }{ AB }=\frac{ AB }{ AD }\] (read as: one side in first triangle : same side in other one= same number.

Because in the above equation, you know 3 out of four lengths, you can calculate the fourth (AD). Once AD is known, you get CD = AD-16.