Question

What is the length of line AB?

a. 8
b. 8.3
c. 6.6
d. 9.7

Wait as I draw the problem.

Answer 1

The line.

Answer 2

This problem is most easily solved by looking at ratios of similar triangles. First, get the length of AD, That can be derived from the Pythagorean Theorem where:

(AD)^2 + 4^2 = 5^2

so, once you have that, which is part of the key, then you can use similar triangles:\[\frac{ AD }{ 5 } = \frac{ 5 }{ AB }\]

Now, you will have AB.

Answer 3

But, how do I figure out AD?

Answer 4

The similar triangles comes about through AAA, looking at triangles ADC and ACB. The two triangles share angle A and a 90-degree angle, so the last corresponding set of angles are equal.

You figure out AD from that first equation I gave to you. Get 4^2 over to the right by subtracting it from each side and then take the square root.

Answer 5

Rewrite

(AD)^2 + 4^2 = 5^2

by subtracting 4^2 from each side. Can you do that?

Answer 6

You can make this a little easier by first resolving 4^2 and 5^2. What are 4^2 and 5^2?

Answer 7

16 and 25

Answer 8

Good, now get 16 over to the right by subtracting 16 from each side. Then take the square root.

Answer 9

It gave me the square root of 9.

Answer 10

And that would equal 3.

Answer 11

Good, now all you have left to do is that second equation which is the ratios.

Answer 12

The answer is 8.3 !

Answer 13

Thank youuu

Answer 14

uw! And thx for the recognition!