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This printable supports Common Core Mathematics Standard HSG-SRT.C.7

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# Sine and Cosine of Complementary Angles (Grades 11-12)

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## Sine and Cosine of Complementary Angles

1.
In a right triangle, the two non-right angles are ALWAYS complementary.
1. True
2. False
2.
Right triangles are NEVER obtuse.
1. True
2. False
3.
In $Delta ABC$, which of the following is/are equal to $(AB)/(BC) ?$ There may be more than one correct answer.
1. $sin(B)$
2. $sin(C)$
3. $cos(B)$
4. $cos(C)$
4.
In $Delta ABC$, which of the following is/are equal to $cos(C) ?$ There may be more than one correct answer.
1. $(AC)/(BC)$
2. $sin(B)$
3. $cos(B)$
4. $(AB)/(BC)$
5.
In $Delta ABC$, which of the following is/are equal to $sin(A) ?$ There may be more than one correct answer.
1. $cos(B)$
2. $cos(90° - A)$
3. $sin(90° - B)$
4. $sin(B)$
6.
In $Delta ABC$, which of the following is/are equal to $(AB)/(BC) ?$ There may be more than one correct answer.
1. $sin(C)$
2. $cos(B)$
3. $sin(90°-B)$
4. $cos(90°-C)$
7.
$Delta FGH$ is a right triangle and $ang G$ is a right angle. If $cos(F) = cos(H)$, what are the measures of the acute angles in this triangle?
1. They are both equal and can be anything less than 45° (and greater than 0°).
2. They are both 45°.
3. The angles measures are 30° and 60°.
4. No such triangle exists.
8.
$Delta XYZ$ is a right triangle and $ang Y$ is a right angle. If $cos(2X) = sin(X)$, what are the measures of the acute angles in this triangle?
1. The angles measures are 30° and 60°.
2. The angle measures are 22.5° and 45°.
3. Only the measure of $ang X$ can be determined, and it is 30°.
4. There is no such triangle.
9.
Referring to $Delta ABC$, what is the value of $(sin(B)+cos(C))/2$, fully simplified?
1. $(AC)/(2BC)$
2. $(AC+AB)/(2BC)$
3. $(AB)/(BC)$
4. $(AC)/(BC)$
10.
Referring to $Delta ABC$, what is the value of $sin^2(B) + sin^2(A)$, fully simplified?
1. $(2AC^2)/(AB)^2$
2. $(2BC^2)/(AB)^2$
3. $1$
4. $2/(AB)$
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