Question 230346: How do you find the perimeter of a right triangle when all they give me is that one angle equals 60 degrees and the hypotnuse is 48 cm? Thanks for your time
Found 3 solutions by rfer, texttutoring, solver91311:
Answer by rfer(16322)   (Show Source):
Answer by texttutoring(324)  (Show Source):
You can put this solution on YOUR website! Use trigonometry ratios, Sine and Cosine.
Remember that Sine(angle) = Opposite/Hypotenuse and Cosine(angle) = Adjacent/Hypotneuse.
Let the other 2 sides of the triangle be x and y.
sin(60) = x /48
48*sin(60) = x
x = 41.6 cm
cos(60) = y /48
48*cos(60) = y
y = 24 cm
Perimter = 48 + x + y
Perimeter = 48 + 41.6 + 24
Perimter = 113.6 cm
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
If you know the measure of one of the acute angles of a right triangle, you know the measure of all three angles. The sum of the angles of a triangle is 180. You are given one of the angles as 60, and you are given that it is a right triangle so another of the angles must be 90, leaving 30 for the measure of the third angle. A 30-60-90 right triangle has the property that the side opposite the 60 degree angle is one-half the measure of the hypotenuse. (This should make sense if you think about setting two 30-60-90 triangles next to each other with the long legs together. The two short legs will form the third side of an equilateral triangle, hence their sum is equal to the hypotenuse of the 30-60-90.)
Now, consider Pythagoras. If you have a 30-60-90 triangle with a hypotenuse of 1, then the short leg is  , hence the long leg must be ^2}\ =\ \frac{\sqrt{3}}{2}) . Using the properties of similar triangles we now know that the three sides of your triangle are  ,  , and  .
Just add 'em up. Leave your answer in terms of  for the exact answer, or use your calculator to determine an appropriately precise numerical approximation.
John
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