anonymous 5 years ago 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)

1. anonymous

x = 4 and y =3

2. anonymous

ops, my mistake

3. anonymous

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

4. anonymous

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

5. anonymous

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

6. anonymous

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 =$5\sqrt{7}$

7. anonymous

I'm making so much mistakes today... sorry for cos(B) it is actually adj / hyp so the adjacent side is 15/4

8. anonymous

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

9. anonymous

sin(b) =$\sqrt{1-\cos^2(B)}$ so it is $\sqrt{7/4}$

10. anonymous

sqrt(7) / 4

11. anonymous

thanks everybody! =]

12. anonymous

メダルくれたら嬉しいんだけど。