Understanding Trig Ratios in Right Triangles (Grades 11-12)
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Understanding Trig Ratios in Right Triangles
1.
[math]Delta ABC[/math] is an acute triangle. The sine of angle A can be expressed as [math](BC)/(AC)[/math].

- True
- False
2.
In [math]Delta ABC[/math], [math]ang B[/math] is a right angle and [math]sin(C) = 0.829[/math]. If [math]Delta EFG \ ~ \ Delta ABC[/math], then [math]sin(G) = 0.829[/math].
- True
- False
3.
Two right triangles both have angle measures of 25°, 65°, and 90°, but one triangle has side lengths which are double the lengths of the other triangle. Therefore, the sine of the smallest angle in each triangle will not be equal.
- True
- False
4.
The ratio of the largest leg of a right triangle to its hypotenuse will ALWAYS have the same value for ANY two similar right triangles.
- True
- False
5.
In [math]Delta ABC[/math], as seen below, [math]m ang C < m ang B[/math]. For any triangle that is similar to [math]Delta ABC[/math], the cosine of the smallest angle will be equal to [math](AC)/(BC)[/math].

- True
- False
6.
[math]Delta ABC \ ~ \ Delta EFG[/math], and [math]ang B[/math] and [math]ang F[/math] are right angles. Which of the following is/are definitely true? Choose all correct answers.
- [math]cos(A) = cos(E)[/math]
- [math](BC)/(AC) = (FG)/(EG)[/math]
- [math]sin(A) = sin(E)[/math]
- [math](AB)/(AC) = (EF)/(EG)[/math]
7.
[math]Delta ABC \ ~ \ Delta XYZ[/math], and [math]ang C[/math] and [math]ang Z[/math] are right angles. Which of the following is/are definitely true? There may be more than one correct answer.
- [math]sin(X) = (BC)/(AB)[/math]
- [math]tan(B) = (XZ)/(YZ)[/math]
- [math]cos(A) = (AC)/(XY)[/math]
- [math]tan(A) = (BC)/(XZ)[/math]
8.
[math]Delta CDE \ ~ \ Delta HJK[/math], and [math]ang D[/math] and [math]ang J[/math] are right angles. Which of the following is/are definitely true? Choose all correct answers.
- [math]sin(E) = (CD)/(CE)[/math]
- [math]cos(E) = (DE)/(HK)[/math]
- [math]sin(K) = (CD)/(CE)[/math]
- [math]cos(K) = (DE)/(CE)[/math]
9.
[math]Delta EGH \ ~ \ Delta LMN[/math], and [math]ang E[/math] and [math]ang L[/math] are right angles. Which of the following is/are definitely true? Choose all correct answers.
- [math]sin(G) = sin(M)[/math]
- [math]GH = MN[/math]
- [math]EH = LN[/math]
- [math](EH)/(GH) = (LN)/(MN)[/math]
10.
[math]Delta ABC[/math] and [math]Delta QRS[/math] are both right triangles, where [math]ang B[/math] and [math]ang R[/math] are right angles. If [math]cos(C) = cos(S)[/math], which of the following is correct?
- [math]Delta ABC[/math] must be congruent to [math]Delta QRS[/math].
- [math]Delta ABC[/math] must be similar to [math]Delta QRS[/math].
- [math]Delta ABC[/math] and [math]Delta QRS[/math] may or may not be similar, but there's not enough information to be certain.
- [math]Delta ABC[/math] and [math]Delta QRS[/math] are not similar.
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