Question

In triangle ABC below, what is the measure of angle B? In particular, which option below gives an exact expression for angle B and an approximation that is correct to the nearest tenth of a degree?
a) sin-1 (3/4) =48.6 degrees
b) cos-1 (3/4) = 41.4 degrees
c) tan-1 (3/4) = 36.9 degrees
d) tan-1 (4/3) = 53.1 degrees

Answer 1

your problem mentions `In triangle ABC below` but I don't see any drawing. Please post the drawing

Answer 2

Thanks

Answer 3

Hint:
segment AC is the side opposite angle B
AC = 3 is the opposite side

AB is the hypotenuse
AB = 5


\[\Large \sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\]

\[\Large \sin(B) = \frac{\text{AC}}{\text{AB}}\]

\[\Large \sin(B) = \frac{3}{4}\]

Answer 4

thanks!

Answer 5

just wasnt sure which one to use. sin, tan, or cos because i wasnt sure which sides were which

Answer 6

the hypotenuse is ALWAYS the longest side of any right triangle. It is ALWAYS opposite the 90 degree angle since 90 degree is the largest angle (of any right triangle)

so the hypotenuse will not change based on which angle you pick. Only the "opposite" and "adjacent" side labels will change depending on if you pick B or A as your reference angle

Answer 7

B is the reference angle,so the side opposite it is AC. It's opposite because it's as far as you can get from angle B.

side BC is the adjacent side because it's the leg closer to the angle B. It's near or touching angle B

Answer 8

once you determine the reference angle and set up the proper labels, you would use SOH CAH TOA to determine which trig function you would use

http://www.mathwarehouse.com/trigonometry/images/sohcohtoa/sohcahtoa-all.png