What are the angles of isosceles triangle ABC?

[xyz_1965]

In isosceles triangle ABC, the sides are of length AC = BC = 8 and AB = 4. Find the angles of the triangle . Express the answers both in radians, rounded to two decimal places, and in degrees, rounded to one decimal place.

Solution:

I think dropping a perpendicular line from the vertex at C gives me two congruent triangles.

cos(A) = cos(B) = 2/8 = 1/4.

arccos(1/4) = 75.5 degrees

So, angle A = angle B = 75.5 degrees, rounded to nearest one decimal place.

Angle C = 180 - 2arccos(1/4) = 29 degrees, rounded to nearest one decimal place.

I can do the same calculations in radians:

arccos(1/4) = 0.97 radians

So, angle A = angle B = 1.32 radians, rounded to two decimal places.

Angle C = pi - 2arccos(1/4) = 0.51 radians, rounded to two decimal places.

I hope to be right. The answers are not given in the back of the book for even number questions.

 

[jvicens]

I can confirm that your calculations are correct. Dropping a perpendicular line from the vertex at C does indeed give two congruent triangles, making angle A and B equal. Your calculations for the angles in both degrees and radians are accurate. Keep up the good work!