Question

AC is tangent to circle B. BA is a radius of circle B and A is a point of tangency. If AB is equal to 15 and BC is equal to 50, what is the approximate measure of segment AC?

Answer 1

This is a job for the Pythagorean theorem! We've got a right triangle (because the line AC is tangent to AB, it forms a right angle), and we know one leg (AB = 15) and the hypotenuse (BC = 50). The Pythagorean theorem says the square of the length of the hypotenuse will be the sum of the squares of the lengths of the other two sides, so if we let \(x\) be the unknown side,

\[15^2 + x^2 = 50^2\]
Rearrange that to get \(x^2)\ alone on one side, then take the square root to find the value of \(x\), which is the approximate measure of AC.

Answer 2

Ah, @#$#@%.

Rearrange that to get \(x^2\) alone on one side, then take the square root to find the value of \(x\), which is the approximate measure of AC.

Answer 3

I keep getting 52.2, What did you get??

Answer 4

Can you show your work? I get something different.

Answer 5

15^2+50^2=2725 sqare root that =52.2

Answer 6

If you think about it, the hypotenuse is the longest side of the triangle, so 52.2 can't be correct if the hypotenuse is only 50...

Answer 7

What is 15*15? How about 50*50?

Answer 8

225 and 2500

Answer 9

Okay. Now let's look at the equation again:
\[15^2+x^2=50^2\]To get \(x^2\) alone, we need to subtract \(15^2\) from both sides:
\[15^2+x^2-15^2=50^2-15^2\]\[x^2=50^2-15^2\]
now what do you get for \(x\)?

Answer 10

ahhhhh i see 47.6

Answer 11

47.7 rounded

Answer 12

Actually, if you're rounding to 1 decimal place, it should be 47.7...

Answer 13

Snap :-)

Answer 14

Yes thanks for u help. I really appreciate it

Answer 15

You're welcome!