SOLUTION: I am given a right triangle with angle measures of 15 and 75 degrees. The side opposite the 15 degree angle is 2 units long. The question asks me to calculate the exact length o
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Question 750137: I am given a right triangle with angle measures of 15 and 75 degrees. The side opposite the 15 degree angle is 2 units long. The question asks me to calculate the exact length of the hypotenuse in radical form.
I doubled the 15 degree angle and created a 30-60-90 triangle so I know the new hypotenuse is twice the new short side, and that the common long side is root three times the short side. I also have the Pythagorean relations for the two right triangles, so I have a system of equations, but my system resolves to an identity. I need to introduce some new information.
Thanks, John
Found 3 solutions by FrankM, Alan3354, MathTherapy:
Answer by FrankM(1040) (Show Source): You can put this solution on YOUR website!
Remember SOHCAHTOA
Sin15=2/hypotenuse
this is ~ 7.727
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
I am given a right triangle with angle measures of 15 and 75 degrees. The side opposite the 15 degree angle is 2 units long. The question asks me to calculate the exact length of the hypotenuse in radical form.
----------------
c is the hypotenuse
sin(15) = 2/c
c = 2/sin(15)
------
Use the Half-Angle formula to get sin(15)
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
I am given a right triangle with angle measures of 15 and 75 degrees. The side opposite the 15 degree angle is 2 units long. The question asks me to calculate the exact length of the hypotenuse in radical form.
I doubled the 15 degree angle and created a 30-60-90 triangle so I know the new hypotenuse is twice the new short side, and that the common long side is root three times the short side. I also have the Pythagorean relations for the two right triangles, so I have a system of equations, but my system resolves to an identity. I need to introduce some new information.
Thanks, John
The easiest method is to use the difference of angles formula.
sin (A – B) = Sin A Cos B – Cos A Sin B
sin (60 - 45) = Sin 60 Cos 45 – Cos 60 Sin 45
sin = Sin 60 Cos 45 – Cos 60 Sin 45
Length of hypotenuse = , or (in simplest radical form)
You can do the check!!
Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
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