Question

Need Help!!! ill give metals for it. Find the six trigonometric ratios for A. Show your work and make sure your answers are rationalized. The picture of the question is below in the comments.

Answer 1

Heres the image of the question.

Answer 2

@jim_thompson5910

Answer 3

@TylerMckinney16 Do you know how to find the length of segment AB

Answer 4

No lol.

Answer 5

have you learned the pythagorean theorem yet?

Answer 6

No not yet

Answer 7

the pythagorean theorem is used to find the length of any missing side of a right triangle

it turns out that if we have a triangle with side lengths a,b,c with c being the longest side, then we can form this equation

\[\Large a^2 + b^2 = c^2\]

Answer 8

In this case, a = 4 and b = 7 are the two known sides. They are called legs of the right triangle

the hypotenuse (the longest side) is unknown, so c is unknown

Answer 9

\[\Large a^2 + b^2 = c^2\]

\[\Large 4^2 + 7^2 = c^2\]

\[\Large 16 + 49 = c^2\]

I'll let you finish and solve for c

Answer 10

Ok thank you.

Answer 11

tell me what you get for c and then we can move onto the next step

Answer 12

Sounds great

Answer 13

I cant find it.

Answer 14

what is 16+49 equal to?

Answer 15

65

Answer 16

so we'll have

\[\Large 65 = c^2\]

\[\Large c^2 = 65\]

Answer 17

we want the value of `c` and not `c^2`

to undo the square, we apply the square root to both sides

Answer 18

\[\Large c^2 = 65\]

\[\Large \sqrt{c^2} = \sqrt{65}\]

\[\Large c = \sqrt{65}\]

Answer 19

The length of segment AB is exactly \(\Large \sqrt{65}\) units

use a calculator and tell me what the square root of 65 is equal to (approximately)

Answer 20

8?

Answer 21

it's going to be slightly larger than 8

it's going to be some decimal value

what does your calculator say?

Answer 22

8.0622577483 ????

Answer 23

Thats what it says.

Answer 24

I'm getting the same

so AB is roughly 8.0622577483 units long

we'll stick with the exact form though when it comes to the trig values