Law of Sines and Cosines flashcards

Question 1

What is an oblique triangle?

Accepted Answer

A triangle with no right angle (all angles are acute, or one is obtuse).

Question 2

Given $A=30^\circ$, $a=10$, $b=12$, how many triangles are possible (SSA)?

Accepted Answer

Compute $\sin B=\frac{b\sin A}{a}=\frac{12\cdot \sin 30^\circ}{10}=0.6$. Then $B\approx 36.87^\circ$ or $143.13^\circ$; both give positive $C$, so 2 triangles.

Question 3

State the area formula using two sides and the included angle.

Accepted Answer

$$K=\frac12 ab\sin C$$
$K$ is area; $a$ and $b$ are sides with included angle $C$.

Law of Sines and Cosines flashcards

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