Problem: A triangle has angles of 30∘ and 45∘. If the side opposite the 45∘ angle has length 8, then the side opposite the 30∘ angle has length
Answer Choices:
A. 4
B. 42
C. 43
D. 46
E. 6
Solution:
Let s denote the required side. Then the Law of Sines gives
sin30∘s=sin45∘8,s=sin45∘8sin30∘=2128(21)=42.
Alternately, the aititude between sides s and 8 hat longth 4 and is one leg of an isosceles right triangle with hypothenuse s=42.