SOLUTION: topic: 30-60-90 triangle in geometry
a triangle with sides 12 and 15 intercepts an angle of 60 degrees. Find the third side.
NOTE: Letters to represent sides dont mater in t
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Question 136192: topic: 30-60-90 triangle in geometry
a triangle with sides 12 and 15 intercepts an angle of 60 degrees. Find the third side.
NOTE: Letters to represent sides dont mater in this problem
Answer by jojo14344(1513) (Show Source): You can put this solution on YOUR website!
There could be 2 ways to solve this,
first if it follows your pattern of 30-60-90 deg as the included angle and side a= 12 (adjacent side) which intercept at side b = 15 (hypotenuse) at an angle 60deg. Then you can solve it by the pythagorean theorem, where side c (opposite side) will be the other side.
so,
a^2 + c^2 = b^2
c^2= b^2 - a^2
c^2=(15)^2 - (12)^2
c = 9
or, if it does not follow your included angle 30-60-90, then you have to use cosine law with the following given;
a=12 c= ? (opposite side of angle C)
b=15
C = 60 deg
then,
c^2 = (a^2 + b^2 - 2ab cos C)
c^2 = (12)^2 + (15)^2 - 2(12)(15)cos60
c= 13.75
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