Question

How do you calculate the size of an angle, given the three sides a=5, b=4, c=3?

Answer 1

You know this is a right triangle because `3^2 + 4^2 = 5^2` .
Thus, the side whose length is 5 must be the hypotenuse (it's the largest length.) To find the measure of the angle between the hypotenuse and the side length of 4, you can use the cosine function.

cos `θ` = `"adjacent"/"Hypotenuse"`

so...

cos `θ` = `4/5` = 0.8

thus...

`cos^-1` cos (`θ`) = `cos^-1`(0.8)

`θ` = `cos^-1`(0.8) = 36.8698 = 36.87

To conclude, the angle between the hypotenuse and the side whose length is 4 is 36.87. To find the length of the other side, you can subtract the total degree measure of a triangle by 90 (it's a right triangle so at one angle must be 90 degrees.)

total degree measure - the right angle - the angle you just found = the last angle

180 - 90 - 36.87 = 53.13

To conclude, the two angles are 36.87 and 53.13.