anonymous 3 years ago 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.)

1. anonymous

2. anonymous

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...

3. anonymous

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

4. anonymous

16 = a, 30 = c?

5. anonymous

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

6. anonymous

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

7. anonymous

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.

8. anonymous

So AB=34.

9. anonymous

Now what do I do to find CD?

10. anonymous

@ZeHanz

11. anonymous

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.