Trig: sin-cos-tan question

Stacy is flying a kite with a string that is 220ft. The kite is currently 135ft off the ground. What is the measure of the angle formed by the kite and the ground?

sinθ=135/220
θ=sin^-1(135/220)
θ≈37.9º

Hope this helps!

A kite usually flies in the air with the string rising diagonally, so that makes a right triangle. The string, being diagonal is the HYPOTENUSE. The off-the-ground-distance is essentially the OPPOSITE side of the triangle, since it is opposite the angle you need to measure.

Since we need to find the angle and we have only the opposite and the hypotenuse, we need sine. If you have been introduced to inverses, then we really need arcsine, the inverse of sine.

So:
sineA = opposite/hypotenuse
sineA = 135 / 220
sineA = .6136 (infinite)
arcsine(sine(A))= arcsine(.6136)
A ~ 37.8529 Degrees

An easy way to remember the trig equations, SOH CAH TOA
SOH for SIN=opposite over hypotenuse
CAH for COS= opposite over hypotenuse
TOA for TAN = opposite over adjacent

If you draw a picture you see that the string is the hyp. and the height is the opposite side.

sin(t) = 135 / 220
sin(t) = 27 / 44
t = arcsin(27 / 44)
t = 37.852902732343683699490484144391

It's the angle whose sin is 135/220.

Arc sin .614.