Triangles 1 and 2 are similar What ratio relates a side length of triangle 1 to the corresponding side length of triangle 27. Fi
ll the box to complete the ratio.
___ to 12
___ to 12
2 answers:
First we have to see the name of similar triangles. And here triangles, CBA and FED are similar . Now we need to use the property of similar triangle, which is
Corresponding sides of similar triangles are in same proportion. Therefore in triangle FED, 12 is the measurement of side opposite to angle with measurement 28 . So in triangle CBA, side opposite to angle of measurement 28 is of length 8 .
So the ratio is
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<h3>2 Answers: Choice C and Choice E</h3>
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Explanation:
θ = greek letter theta = reference angle
Using the unit circle, you should find that when θ is pi/3, we have
- cos(θ) = cos(pi/3) = 1/2
- sin(θ) = sin(pi/3) = sqrt(3)/2
Dividing sine over cosine gets us tangent
tan(θ) = sin(θ)/cos(θ) = sqrt(3)/2 divide over (1/2) = sqrt(3)
Effectively, the denominators '2' cancel out when dividing the two fractions. The result we get here is not sqrt(3)/2, so we can rule out choice A.
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Choice B can be ruled out because
cos(0) = 1
sin(0) = 0
So,
tan(0) = sin(0)/cos(0) = 0/1 = 0
which doesn't match with y = pi
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Following the same ideas as mentioned before:
cos(pi/4) = sqrt(2)/2
sin(pi/4) = sqrt(2)/2 ... it's not a typo, sine and cosine are the same here
tan(pi/4) = 1 after dividing the two items above
We end up with y = 1 as the screenshot shows, so (pi/4, 1) is one point on the graph of y = tan(x).
Choice C is one of the answers
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Choice D however is not one of the answers because
sin(pi/2) = 1
cos(pi/2) = 0
tan(pi/2) = undefined, because the denominator cosine is 0 in this case
So there's a vertical asymptote at x = pi/2 for y = tan(x)
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Choice E is another answer, because,
sin(pi) = 0
cos(pi) = -1
tan(pi) = sin(pi)/cos(pi) = 0/(-1) = 0
This shows (pi, 0) is a point on y = tan(x).
The graph is shown below. Points C and E are on the blue tangent curve, while everything else isn't.
I used GeoGebra to create the graph. Desmos is also a handy tool that can perform similar tasks.