What is sin 60 degree
1 answer:
Okay, notice one thing right off the bat? 60 degrees on a right triangle (unit circle w/ terminal arm) will create the infamous 30-60-90 triangle.
We can use this to our advantage. Since sin is the y-coordinate on the unit circle. We need to solve for the longest side of a 30-60-90 triangle.
We find that the long side (y) of our 30-60-90 triangle is sqrt(3)/2. Since this is in quadrant 1, we know it is positive.
So -- sin60° = sqrt(3)/2
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Answer:
.894
Step-by-step explanation:
First thing to do is to solve for the height of the triangle, BD. That's easy. We have the length of the hypotenuse and the base, so Pythagorean's Theorem gives us that the height is 8.003255588 which rounds nicely to 8. Now you have to call on the fond memories you have of the geometric mean in right triangles to solve the rest. For the sin of x you need the hypotenuse of that smaller right triangle on the left, side AB. First let's use geometric mean to find AD. The formula for that, now that we know the height, is
Filling that in with numbers we have
and
64 = 16(AD). Solve for AD to get that AD has a length of 4. Now we know two of the three sides in that smaller triangle on the left and can solve for the hypotenuse.
and
so
c=√80 which simplifies to 4√5. That means that the sin ratio for x is
which divides out to .894