Question

Find the values of the sine, cosine, and tangent for angle A

Answer 1

first we need to figure out the length of that 3rd side

Answer 2

First find the length of the hypotenuse, AB, using Pythagorean Theorem,
leg^2 + leg^ = hypotenuse^2
24^2 + 36^ 2 = x^2
576 + 1296 = x^2
1872 = x^2
x = sqrt(1872)


Now, sin A = length of the opposite leg/hypotenuse = 24/sqrt(1872)
cos A = length of adjacent leg/hypotenuse = 36/sqrt(1872)
tan A = length of opposite leg/adjacent leg = 24/26 or 2/3 in reduced form

Answer 3

length of the 3rd side (calling it BA ) would be\[(BA)^2 = 24^2 + 36^2\]\[BA = \sqrt{24^2 + 36^2}\]

Answer 4

And the rest can be found above

Answer 5

none of those are answer choices, that's why i'm confused. I got that far but can't get an answer that's a choice.

Answer 6

Alright ill continue and see what happens

Answer 7

could be they broke down sqrt(1872)

Answer 8

You're welcome.

Answer 9

so \[BA = \sqrt{1872}\]\[\sqrt{1872} = 12\sqrt{13}\]

Answer 10

as Tyler1992 just showed above.

Answer 11

thank you guys for helping me btw

Answer 12

okay, I don't know why I didn't think about it breaking down further

Answer 13

so \[\tan(A) = \frac{24}{36} = \frac{2}{3}\]