Answer:
(a) sin⁻¹(√35/14)
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relations between sides and angles in a right triangle. Here, the given sides AB and AC are the side opposite angle C, and the hypotenuse (opposite right angle B). That means the relevant relation is ...
Sin = Opposite/Hypotenuse
sin(C) = AB/AC
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For this problem, substituting values gives ...
sin(C) = (3√5)/(6√7) = (1/2)√(5/7) = (1/2)(√35)/7 = (√35)/14
C = arcsin((√35)/14)
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<em>Additional comment</em>
Choice B can be eliminated on the grounds that the fraction is not reduced to lowest terms. Choices C and D are eliminated because they assume a cosine relation is involved. That is, you can choose the correct answer based on SOH CAH TOA without concerning yourself with the details of the radical expression.
40% chance yellow 35% brown
The first and the third statements describe Jan's situation.
Answer:
and 
.
Step-by-step explanation:
So I believe the problem is this:
where we are asked to find values for 
and 
such that the equation holds for any 
in the equation's domain.
So I'm actually going to get rid of any domain restrictions by multiplying both sides by (x-3)(x+7).
In other words this will clear the fractions.
As you can see there was some cancellation.
I'm going to plug in -7 for x because x+7 becomes 0 then.
Divide both sides by -10:
Now we have:
with
I notice that x-3 is 0 when x=3. So I'm going to replace x with 3.
Divide both sides by 10:
So and .
