Question

right triangle has angle A and B. Cos B=3/4
the hypotenuse is 5. find x (opposite) and y (adjacent) the B is above the 90 degrees, and A is next to it (sorry hard to explain cause there's a drawing)

Answer 1

x = 4 and y =3

Answer 2

ops, my mistake

Answer 3

cosB = adj/hyp = y/5
cosB = 3/4
--> y/5 = 3/4
y=(3*5)/4 = 15/4
use pythagorean theorem to find x
5^2 = (15/4)^2 + x^2
x^2 = 25 -(225/16)
x^2 = (400 - 225)/16
x = 5*sqrt(7)/4

Answer 4

if the hypotenuse is 5, then

cos(B) = opposite / hypotenuse

= opp / 5

so

3/4 = opp / 5

by multiplying 5 on both sides,

opp = 15/4

Answer 5

haha i almost made same mistake when i saw 3/4 :)

Answer 6

now if you want to find the adj, you use sin(B)
or just use the pythagorean thm.

\[5^2 = (15/4)^2 + adj^2\]

or

sin(B) = sqrt(7)

so

sin(B) = opposite / hypotenuse

= opp / 5

= sqrt(7)

so opp =\[5\sqrt{7}\]

Answer 7

I'm making so much mistakes today...

sorry

for cos(B) it is actually adj / hyp

so the adjacent side is 15/4

Answer 8

haha. yeah. it's okay, dumbcow explained it. now what if i wanted to find sin(B) would it be (5*sqrt7/4)/5 ?

Answer 9

sin(b) =\[\sqrt{1-\cos^2(B)}\]

so it is \[\sqrt{7/4}\]

Answer 10

sqrt(7) / 4

Answer 11

thanks everybody! =]

Answer 12

メダルくれたら嬉しいんだけど。