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2 years ago

10

Consider the cases SSS, AAS, ASA, SAS, and SSA. For which of these cases are you unable to solve the triangle using only the Law

of Sines?

1 answer:

qwelly [4]2 years ago

7 0

Answer:

SSS and SAS

Step-by-step explanation:

To use the law of sines we need to know two angles and one side or two sides and one angle which should be opposite to one of known sides.

SSS - <u>unable</u> to solve as no angle is known
AAS - two angles and non-included side, able to find the missing angle solve the rest
ASA - two angles and the included side, able to find the missing angle solve the rest
SAS- two sides and the included angle, <u>unable</u> to solve
SSA - two sides and non-included angle, able to find the other angles and solve fully

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So in order to get all the fractions to have a common denominator, we need to multiply $\dfrac k{k-2}$ by $\dfrac{k-6}{k-6}$ , and $\dfrac1{k-6}$ by $\dfrac{k-2}{k-2}$ :

$\dfrac k{k-2}\cdot\dfrac{k-6}{k-6}=\dfrac{k(k-6)}{(k-2)(k-6)}=\dfrac{k^2-6k}{k^2-8k+12}$

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$\dfrac4{k^2-8k+12}=\dfrac{(k^2-6k)+(k-2)}{k^2-8k+12}$

As long as $k\neq2$ and $k\neq6$ (which we can't have because otherwise $k^2-8k+12=0$ ), we can cancel $k^2-8k+12$ in the denominators on both sides:

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We can factorize the right side:

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