Question 253344: need to find the hypotenuse of a triangle. It has a 15, 90 and 85 degree angle. One side of the triangle is measured 48 yards.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! sum of the interior angles of a triangle = 180.
your angles sum up to be 105 + 85 = 190.
something is not right.
assuming your 85 degree angle is really 75 degrees, then the sum of the angles would be correct.
you would still have a problem because you didn't identify which side was 48 yards.
some assumptions would need to be made, i.e. which side was 48 yards.
assuming that this is a right triangle, then we can assume the 48 yards is either opposite the 15 degree angle, or it is opposite the 75 degree angle (if the assumption of that angle being 75 degrees is accurate).
since this is a right triangle, we can use sine or cosine functions to find the hypotenuse.
let the angle we are working with be the 75 degree angle.
if 48 yards is opposite this angle, then sin(75) = opposite/hypotenuse.
multiply both sides of this equation by hypotenuse and divide both sides of this equation by sin(75) to get:
hypotenuse = opposite/sin(75) = 48/sin(75) = 49.69325666
if 48 yards is adjacent this angle, then cos(75) = adjacent/hypotenuse.
multiply both sides of this equation by hypotenuse and divide both sides of this equation by cos(75) to get:
hypotenuse = adjacent/cos(75) = 48/cos(75) = 185.4577586
working from the 15 degree angle you would get the same results.
if 48 is opposite the 15 degree angle, you would get hypotenuse = 48/sin(15) = 185.4577586
if 48 is adjacent the 15 degree angle, you would get hypotenuse = 48/cos(15) = 49.69325666
you need to get the angles right to start with.
then you need to determine which side is 48 yards long.
once you do that, you can use the trigonometric functions of sine and / or cosine to find the hypotenuse.
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