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This printable supports Common Core Mathematics Standard HSF-TF.A.3

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# Trig Ratios and Special Triangles (Grades 11-12)

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## Trig Ratios and Special Triangles

1.
For triangle ABC, if $tan(B) = 1/sqrt(3)$, then its angle measures are either $30°-60°-90°$ or $45°-45°-90°.$
1. True
2. False
2.
For triangle $ABC$, $cos(B) = 1/sqrt(3)$. Therefore, the angle measures of this triangle are either $30°-60°-90°$ or $45°-45°-90°$.
1. True
2. False
3.
For triangle ABC below, if $sin(B) = sqrt(2)/2$, its angle measures are either $45°-45°-90°$ or $30°-60°-90°.$
1. True
2. False
4.
The side lengths of $Delta ABC$ are $AB = 1 \ "unit", \ AC = sqrt(3) \ "units", BC = 2 \ "units"$. What is the value of $sin(C) ?$
1. $1/2$
2. $sqrt(3)/2$
3. $1/sqrt(3)$
4. $sqrt(3)$
5.
The side lengths of triangle ABC are: $AB = 1 \ "unit", \ AC = 1 \ "unit", \ BC = sqrt(2) \ "units"$. What is the value of $tan(B) ?$
1. $sqrt(2)$
2. $1/sqrt(2)$
3. $0$
4. $1$
6.
The side lengths of triangle ABC are as follows: $AC = 4sqrt(3) \ "units", \ BC = 4 \ "units", \ AB = 8 \ "units"$. What is the value of $cos(A) ?$
1. $4/sqrt(3)$
2. $1/2$
3. $sqrt(3)/2$
4. $sqrt(3)/8$
7.
The side lengths of triangle ABC are as follows: $AB = (2sqrt(3))/3 \ "units", \ BC = sqrt(3)/3 \ "units", \ AC = 1 \ "unit"$. What is the value of $tan(B) ?$
1. $1/sqrt(3)$
2. $sqrt(3)$
3. $(2sqrt(3))/3$
4. $sqrt(3)/2$
8.
For triangle ABC, $cos(C) = 1/sqrt(2)$. What is the value of $BC$ if $AC = sqrt(3) \ "units"?$
1. $sqrt(2) \ "units"$
2. $sqrt(3)/2 \ "units"$
3. $sqrt(6) \ "units"$
4. $1 \ "unit"$
9.
In triangle ABC, $sin(C) = 1/2$. If $AC = 6 \ "units"$, what is the length of $bar{BC} ?$
1. $2 \ "units"$
2. $2sqrt(3) \ "units"$
3. $12 \ "units"$
4. $4sqrt(3) \ "units"$
10.
In triangle ABC $tan(B) = sqrt(3)$. What is the length of $bar{BC}$ if $AB = 1/4 \ "unit" ?$
1. $1/8 \ "unit"$
2. $sqrt(3)/12 \ "units"$
3. $4 sqrt(3) \ "units"$
4. $1 \ "unit"$
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