A triangle with the hypotenuse measuring 8, and the short leg measuring 5, and the the long leg measuring 7. How do you find the angles C the top angle, B the lower right angle, A the left angle?

1 Answer
Dec 17, 2015

Answer:

Ignoring the (false) implication that we are dealing with a right angled triangle, we can use the Law of Cosines to determine the 3 angles

Explanation:

I have assumed that the triangle looks like:
enter image source here
The reference to a hypotenuse implies a right-angled triangle but based on the Pythagorean Theorem this is clearly false.

The Law of Cosines for a triangle with sides #a, b, c# and corresponding opposite angles #A, B, C# is
#color(white)("XXX")c^2=a^2+b^2-2ab*cos(C)#

which can be re-arranged as:
#color(white)("XXX")cos(C)=((a^2+b^2)-c^2)/(2ab)#
or
#color(white)("XXX")C = arccos(((a^2+b^2)-c^2)/(2ab))#

and similarly for angles #A# and #B#

Plugging in the values for #a, b, c# (I would suggest using a calculator or spreadsheet), we get

In radians
#color(white)("XXX")A=1.047, B=1.427, C=0.667#

In degrees
#color(white)("XXX")A=60^@, B=81.8^@, C=38.2^@#