MathDB

11

Part of 2019 India PRMO

Problems(2)

Trigonometry and Triangles

Source:

8/11/2019
How many distinct triangles ABCABC are tjere, up to simplilarity, such that the magnitudes of the angles A,BA, B and CC in degrees are positive integers and satisfy
cos⁡Acos⁡B+sin⁡Asin⁡Bsin⁡kC=1\cos{A}\cos{B} + \sin{A}\sin{B}\sin{kC} = 1
for some positive integer kk, where kCkC does not exceet 360∘360^{\circ}?
trigonometry
Easy SFFT

Source: PRMO 2019 Leg 2 P11

8/25/2019
Find the largest value of aba^b such that the positive integers a,b>1a,b>1 satisfy abba+ab+ba=5329a^bb^a+a^b+b^a=5329
algebraPRMOSFFT