Question

If = 27° and x = 9 cm, what is the value of y to the nearest tenth of a centimeter? alpha is equal to 27 degrees by the way

Answer 1

What equals 27 degrees? I think you forgot to put it in

Answer 2

Do you have any other info? Is there a circle involved or something?

Answer 3

so its a triangle with a right angle on the bottom right, alpha is at the very top, theta is at the bottom left, x is on the bottom outside horizontal line and z is outside on the left side (hypotenuse) and y is outside on the right

Answer 4

ok, thanks :)
one moment

Answer 5

could u write ur steps down as well

Answer 6

yes

Answer 7

ok. So The first thing you want to do when solving a triangle is to identify how many sides and angles you have and in what pattern. It is AAS (angle-angle-side in this case. Each side always coordinates with the angle across from it. So x coordinates with 27 degrees (X), etc. Now, use the Law of Sines to find the side y:

y/ sin Y = x/ sin X
y/ sin Y = 9/ sin 27

We need to find the angle Y, which is directly across from side y. This part is easy: add 27 + 90 (the angles you have) = 117. Then subtract 117 from 180 = 63.

y/ sin 63 = 9/ sin 27

Use a calculator to find the sines of 63 and 27:

y/ 0.8910 = 9/ 0.4540

Now multiply both sides by 0.8910 to isolate x:

y = (9/0.454) * (0.891/1)
y = 8.019/0.454
y = 17.6630 = 17.7

Answer 8

a good reference: http://www.mathsisfun.com/algebra/trig-solving-triangles.html