Trigonometry: What Do You Need to Do to Your Calculator
Trigonometry: What do you need to do to your calculator?????
1)The base of an isosceles triangle has a length of 16cm. and the vertex angle measures 68º. What is the length of each leg? Round to the nearest tenth of a centimeter.
2)A person at the top of a cliff 100 feet tall sees Gilligan’s boat. His sighting of the boat is at an angle of depression of 10°. How far is the boat from the base of the cliff?
3)An 80-ft-long freeway entrance ramp has a vertical lift of 22 feet. What is the angle of elevation of the ramp?
4)A tree casts a shadow of 28 m. The elevation of the sun is 49°. How tall is the tree?
For 5 – 12, solve for the variable(s).
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KNOW THE UNIT CIRCLE!
You need to know angle measures and be able to answer questions about sine and cosine.
Polygons & Quadrilaterals
Name each polygon. Be as specific as possible.
a)Concave or Convex
b) equilateral , equiangular, regular
c) name by number of sides
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14)
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16)What is the sum of the interior angles of a 24-gon?
17)The measure of one interior angle of a regular polygon is 108°. What is the name of the polygon?
18)What is the measure of one exterior angle of a regular octagon?
19)Two interior angles of a hexagon are 105° and 93°. The other four angles are congruent. Find the measure of the congruent angles
20)Find x
21)List the properties of each of the following: parallelogram, rectangle, rhombus, square, kite, trapezoid, and isosceles trapezoid.
22)Solve for the length ofAD in parallelogram ABCD
23)In isosceles trapezoid WXYZ, WY = 31.4,and ZV =10.8. What is VX?
24)The measure of an exterior angle is shown for each of 3 regular polygons below. Which expression best represents the measure in degrees of an exterior angle of a regular polygon withn sides?
A 30(n + 1)C 30(n − 1)
BD
25)What is the correct name for figure ABCD, with vertices A (2, 1), B (3, 6), C (8, 7), and D (7, 2)?
Answer True/False for questions 14-17.
26)Every square is a rhombus.
27)An equilateral triangle is also isosceles.
28)An decagon has nine sides.
29)Every rectangle is a parallelogram.
Solve for the missing variables.
30)Parallelogram
31)Parallelogram
32)Rhombus
33)Rectangle
Transformations
34)ΔLMN with vertices L(0, 3), M(4, 3), and N(4, 5) is reflected across the x-axis to make ΔL'M'N' and then its image is reflected across the line y = -1 to make ΔL''M''N''. Draw all three triangles on the provided graph, labeling each vertex.
35)An interior decorator represents a wall hangingby a polygon with vertices H(3, 2), A(3, 5), N(8, 5), and G(8, 2). She decides to move the wall hanging toa new location by translating it along the vector . Find the new coordinates of the wall hanging.
36)Given the vertices A(1, 0), B(3, 2), and C(4, 1) rotate the vertices 180o about the origin. Find:
37)Reflect the quadrilateral QUAD across y = -x if Q(-6, 5), U(0, 3), A( -2, -4), and D(-6, -2). State the coordinates of the image:
38)Reflect the function y = x2 + 5 across the x-axis
39)Reflect the line across y = x.Write the equation of the new line:
40)Write the equation of the line of symmetry.
Proportions and Similar Figures
41)
42)Find the following lengths.
For questions 43 and 44, use the picture below to WRITE A PROPORTION and then solve for the missing side.
43)Find TE
44)Find TS
For questions 12 and 13, determine if the two triangles are proportional. Tell why or why not.
45)
46)
Ratios and Proportions
47)The sides of a pentagon are in the ratio 1:1:2:2:3. The perimeter of the pentagon is 45 cm. What is the length of the longest side?
48)Solve the proportion:
49)Dilate quadrilateral W(0,-3) O(-3,6) R(6,6) K(3,-3) with a scale factor of
Write the new coordinates here:
W O R K
Graph the pre-image and image:
50)For the following figures, give the similarity ratio of A to B and scale factor that will dilate from shape A to shape B.
Similarity Ratio:_____ Scale Factor:______
51)Solve the following for the indicated measures. You must use geometric mean.
c = 12; m = 8; a = ?
a = ______
52)Given , find the perimeter and area of.
P=______A =______
53)Prove that the triangles are similar. Find all the lengths to support your proof.
Given: A(3, 1),B(1, 4),C(5, 3),D(1, 7), andE(7, 5)
Prove:ADEABC
Perimeter and Area
54)Find the area in square units of a rectangle that has a width of 4x3y2 and a length of 3x2y3?
55)The area of a rectangle is 144a8b4 square units. If the width of the rectangle is 8a2b2 units, what is the length in units?
56)Find the circumference of a circle whose radius is 12a units.
57)Find the area of a circle whose diameter is 9b units.
58)A diagram of a power/volume control knob on a stereo is shown below.
When the stereo is turned on and the knob is turned to a volume level of 5, the knob is rotated 100°from its off position. What is the approximate arc length of the path traveled by the knob’s rotationfrom the off position to a volume level of 5?
59)If the perimeter of the isosceles trapezoid below is 60 units, what is its area?
60)The shaded area in the circle below representsthe section of a park used by the chamber ofcommerce for a fund-raising event.What is the approximate area of the section ofthe park used for the fund-raiser?
61)Find the area of the shaded region.
62)Find the perimeter and area of the composite figure.
63)Linda has divided her garden into 3 parts, asshown below.What is the area of her garden?
Solids
64)A hexagonal pyramid has volume 400 cm3 and lateral surface area 216 cm2. If its dimensions are multiplied by a scale factor of ½, what will the new volume and lateral surface area be?
For questions 65 – 67, please refer to the following figure.
65)Are all the lateral faces congruent? Why or why not?
66)Find the volume of the pyramid.
67)How many faces, edges, and vertices does the pyramid have?
F = E = ______V =
68)Find the lateral surface area of a cone that has a diameter is 10 inches and a slant height of 7 inches.
69)Find the surface area of a cylinder whose height is 19 cm and whose radius is 8 cm.
70)First find the volume of the composite figure below. Then find the total surface area (what is exposed to the air) of the composite figure.
71)
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Circles
75) = _____
76)x = _____,y = _____, z = _____
77)x = _____
78) =_____ =_____
79) x = ______
Quadratics and Systems
Identify the parent function name and describe the transformation for each function.
80)g(x) = 1/3(x-2)2 + 7
81)f(x) = 5(x + 3)3 – 11
82)f(x) =
Solve the Quadratic.
83)9x2 – 121 = 0
84)6x2 – 7x – 10 = 0
85)2x2 + 14x – 60 = 0
86)10x2 + 25x = 0
Solve each system
87)y = x – 22x – 2y = 4
88)2x + 4y = 10x + 2y = 4
Scratch Work Graphs