Question

3 12 Smaller Triangle Larger Triangle sin = sin = cos = cos = tan 0= tan (= CSC = CSC = sec = sec = cot 8 = cot = Explain why the function values are the same. The triangles are similar so corresponding sides are proportional. The triangles are congruent so the trigonometric function values must be the same.

Answer 1

"P A - 3 o 4 B 0 IQ R 12 in smaller Applying Pythagoras theorem triangle AC = 4 AB²+ BC² larger triangle PR= NPQ+ QR² 12+ 4? N W17 and in ZN 3 ² +12² 3.17 Sino = opposite side Hypotenuse for smaller triangle for larger triangle Sing = AB = Jino. PQ = 3 AC NTY PR 래 3NTY Nir • Cose Adjacent side Hypotenuse for smaller triangle Cose AC NIT BC 4 for larger triangle Cose = QR 12 PR 3N17 Costa 4/N17

• tano opposite side Adjacent side 1 3 12 = 1 for larger triangle; tano = PQ QR for smaller triangle tano AB Be 4 • Csc o = Hypotenuse opposite side for larger triangle Csce = PR/PQ = 3N67/3 = (NIT for smaller triangle CSC o = AC/AB = N17/1 = N17 Secos Hypotenuse adjacent side for larger triangle

SecQ = PRIBRE 3N17/12 - 117/4 for smaller triangle Seco - AC/BC = N174 • Cote- adjacent side opposite side for larger triangle coto= QR/PQ = 12/3= 14 for smaller triangle cotes Bc/AB = 4/1- 4 Triangles are are similar because AB z BC QR AC PR PQ WH 12 3 Ni7 3N17 :) Thus first option is correct: The triangles are similar so the corresponding sides are proportionale 1. The