AnswersMathematics IISimilarity, Right Triangle Trigonometry, and Proof: Part Two

Similarity, Right Triangle Trigonometry, and Proof: Part Two — Test Answers

25 verified answers
1
Free Preview

What is the length of line segment AB ? Round to the nearest tenth.

A
23 point 5 in.
B
68 point 0 in.
C
19 point 3 in.
D
21 point 3 in.
2
Free Preview

If the triangles are similar, which must be true?

A
the fraction with numerator cap r cap y and denominator cap r cap s is equal to the fraction with numerator cap r cap x and denominator cap r cap t is equal to the fraction with numerator cap x cap y and denominator cap t cap s
B
the fraction with numerator cap r cap y and denominator cap y cap s is equal to the fraction with numerator cap r cap x and denominator cap x cap t is equal to the fraction with numerator cap x cap y and denominator cap t cap s
C
the fraction with numerator cap r cap y and denominator cap r cap s is equal to the fraction with numerator cap r cap x and denominator cap r cap t is equal to the fraction with numerator cap r cap s and denominator cap r cap y
D
the fraction with numerator cap r cap y and denominator cap r cap x is equal to the fraction with numerator cap r cap s and denominator cap r cap t is equal to the fraction with numerator cap x cap y and denominator cap t cap s
3

If cosine theta almost equal to 0 point 3 0 9 0 , which of the following represents approximate values of sine theta and tangent theta , for 0 degrees is less than theta comma theta is less than 90 degrees ?

A
sine theta almost equal to 0 point 9 5 1 1 ; tangent theta almost equal to 3 point 0 7 8 0
B
sine theta almost equal to 3 point 2 3 6 2 ; tangent theta almost equal to 10 point 4 7 3 1
C
sine theta almost equal to 0 point 9 5 1 1 ; tangent theta almost equal to 0 point 3 2 4 9
D
sine theta almost equal to 3 point 2 3 6 2 ; tangent theta almost equal to 0 point 0 9 5 5
4

Consider the relationship, given pi over 2 is less than theta comma theta is less than pi sine squared theta plus cosine squared theta is equal to 1 Which of the following best explains how this relationship and the value of sine theta can be used to find the other trigonometric values?

A
The values of sine theta and cosine theta represent the angles of a right triangle; therefore, other pairs of trigonometric ratios will have the same sum, 1 , which can then be used to find all other values.
B
The values of sine theta and cosine theta represent the legs of a right triangle with a hypotenuse of negative 1 , since theta is in Quadrant II; therefore, solving for cosine theta finds the unknown leg, and then all other trigonometric values can be found.
C
The values of sine theta and cosine theta represent the angles of a right triangle; therefore, solving the relationship will find all three angles of the triangle, and then all trigonometric values can be found.
D
The values of sine theta and cosine theta represent the legs of a right triangle with a hypotenuse of 1 ; therefore, solving for cosine theta finds the unknown leg, and then all other trigonometric values can be found.
5

Which equation correctly uses the value of b to solve for A ?

A
tangent of open paren 22.6 degrees close paren is equal to A over 12
B
tangent of open paren 22.6 degrees close paren is equal to 13 over A
C
tangent of open paren 22.6 degrees close paren is equal to 12 over A
D
tangent of open paren 22.6 degrees close paren is equal to A over 13
6

Given right triangle ABC , what is the value of tangent of cap A ?

A
12 fifths
B
5 over 13
C
12 over 13
D
13 over 12
7

If CA is equal to 8 , what is cap c prime cap A prime ?

A
10 units
B
20 units
C
12 units
D
16 units
8

Which value of y would make OP is parallel to LN ?

A
24
B
32
C
36
D
16
9

What are the coordinates of the endpoints of the segment cap t prime cap v prime ?

A
cap t prime times open paren negative 3 comma 6 close paren and cap v prime times open paren 0 comma 1 close paren
B
cap t prime times open paren negative 1 comma 2 close paren and cap v prime times open paren 0 comma 1 close paren
C
cap t prime times open paren negative 3 comma 6 close paren and cap v prime times open paren 0 comma 3 close paren
D
cap t prime times open paren negative 1 comma 2 close paren and cap v prime times open paren 0 comma 3 close paren
10

If triangle YWZ approximates triangle YXW , what is true about angle XWZ ?

A
angle XWZ is a right angle.
B
angle XWZ is congruent to angle XZW .
C
angle XWZ is congruent to angle WXY .
D
angle XWZ is an obtuse angle.
11

Which statements are true about triangle QRS ? Choose three correct answers.

A
The side adjacent to angle cap q is line segment QS .
B
The side adjacent to angle cap r is line segment SQ .
C
The hypotenuse is line segment QR .
D
The side opposite angle cap q is line segment RS .
E
The side opposite angle cap r is line segment RQ .
12

What is the value of y ?

A
3 square root of 3 units
B
6 square root of 3 units
C
9 square root of 3 units
D
12 square root of 3 units
13

What is the scale factor of the dilation?

A
8
B
1 eighth
C
1 fourth
D
4
14

To prove that the triangles are similar by the SAS similarity theorem, it needs to be shown that

A
angle cap c is congruent to angle cap g .
B
the fraction with numerator cap A cap c and denominator cap g cap i is equal to the fraction with numerator cap b cap c and denominator cap h cap i .
C
the fraction with numerator cap A cap c and denominator cap g cap i is equal to the fraction with numerator cap h cap i and denominator cap b cap c .
D
angle cap c is congruent to angle cap c .
15

Why is the information in the diagram enough to determine that triangle LMN approximates triangle PON using a rotation about point cap n and a dilation?

A
because angle MNL and angle ONP are congruent angles
B
because one pair of congruent corresponding angles is sufficient to determine similar triangles
C
because both triangles appear to be equilateral
D
because both triangles appear to be isosceles, angle MNL is congruent to angle ONP , and angle NOP is congruent to angle OPN
16

What is the value of x ?

A
20 units
B
25 units
C
15 units
D
12 units
17

Given right triangle DEF , what is the value of tangent of cap f ?

A
41 ninths
B
40 over 41
C
9 over 41
D
40 ninths
18

A treasure map says that a treasure is buried so that it partitions the distance between a rock and a tree in a ratio of 5 to 9 ratio. Marina traced the map onto a coordinate plane to find the exact location of the treasure. x is equal to open paren the fraction with numerator m and denominator m plus n close paren times open paren x sub 2 minus x sub 1 close paren plus x sub 1 y is equal to open paren the fraction with numerator m and denominator m plus n close paren times open paren y sub 2 minus y sub 1 close paren plus y sub 1 What are the coordinates of the treasure? If necessary, round the coordinates to the nearest tenth.

A
open paren 7 point 6 comma 8 point 8 close paren
B
open paren 11 point 4 comma 14 point 2 close paren
C
open paren 5 point 7 comma 7 point 5 close paren
D
open paren 10 point 2 comma 12 point 6 close paren
19

Which transformations could have occurred to map triangle ABC to triangle cap A double prime cap b double prime cap c double prime ?

A
a dilation and a rotation
B
a reflection and a dilation
C
a rotation and a reflection
D
a translation and a dilation
20

Which value of x would make line segment TV is parallel to line segment QS ?

A
3
B
10
C
11
D
8

Did you find these answers helpful?

More from this Course

Quiz
25 verified answers

Test

practice test
20 verified answers

Practice Test

Quiz
25 verified answers

Test