Similar Triangles & Trig
Are the following triangles similar? if so, state the reason and the scale factor: Triangle ABC is a right triangle: it's legs are 6cm and 8 cm. Triangle DEF is a right triangle: It's legs are 18cm and 24cm.
What is Yes. By SAS, since the right angle is between the two legs and the legs of the triangles have a scale factor of 3.
Solve the following equation by using the quadratic formula: k^2 - 31 -2k = -6 -3k^2 -2k
What is k = 5/2 and k = -5/2
Which of the following is NOT a way to prove triangles congruent: *NOTE* it is okay to have more than one choice for your answer. SSS SSA AA SAS AAS HL
What is SSA and AA.
Convert the following equation between rational and radical form: (3x)^2/4
What is The fourth root of 3x^2
What are the only three theorems we can use to argue two triangles being similar?
What is AA, SSS, SAS
Which function is equivalent to y = x^2 – 6x + 10? A y = (x + 3)2 – 1 B y = (x – 3)2 + 1 C y = (x + 6)2 – 10 D y = (x – 6)2 + 10
What is What is B) y = (x-3)^2 +1
A square with points A (-3,3), B (-3,6), C (-6,3), D (-6,6) is reflected across the x-axis. What are the points of the image of this square?
What is A'(-3,-3) B'(-3,-6) C'(-6,-3) D'(-6,-6)
The length of a rectangular prism is 4sqrt(3) units. The height is 3sqrt(6) units. If the volume is irrational, which could be the measure of the width of the rectangular prism? A 2(sqrt)50 B 4(sqrt)12 C 5(sqrt) 8 D 7(sqrt)18
What is B) 4(sqrt)12
A ship is anchored to a seabed. We know that the rope anchoring the boat is 30 m long, and the angle where the rope meets the seabed is 39 degrees. Use the correct trig identity to find out how deep we would need to go to reach the seabed is. *HINT*- draw a picture!
What is Use sin(39) = x/30 Answer: 18.88 m deep
You have a 500-foot roll of fencing and a large field. You want to construct a rectangular playground area. What are the dimensions of the largest such yard? What is the largest area?
What is A = Lw = (250 – w)w = 250w – w^2 = –w^2 + 250w The largest area will have dimensions of 125 by 125, for a total area of 15,625 square feet
Separate the following angle relationship pairs into two categories: Those which are congruent and those which are supplementary. Corresponding Alternate exterior Vertical Same side interior Same side exterior Alternate interior Linear pair
What is Congruent: Supplementary: Corresponding Same side exterior Vertical Same side interior Alternate exterior Linear pair Alternate interior
The graph of f(x) = 2x2 – 3x + 5 will be translated 8 units down, producing the graph of q(x). Which equation represents the new function, q(x)? A q(x) = 2x^2 – 3x – 3 B q(x) = 2x^2 – 11x + 5 C q(x) = 2x^2 – 3x + 13 D q(x) = 2x^2 + 5x + 5
What is A) q(x) = 2x^2-3x-3
A ladder is leaning up against the wall of a building. The angle where the ladder meets the ground is 30 degrees. If we know the bottom of the ladder is 15 feet of the wall, what is the length of the ladder? *HINT* - use trig identities and draw a picture
What is *SPECIAL TRIANGLE* 30-60-90 ladder length = hypotenuse = 30
The flight of a rocket launched in the air can be modeled by the function f(t) = 2t^2 -7t -3 where t is time in seconds and f(t) is height (in feet) of the rocket. How many seconds will it take for the rocket to return to the ground?
What is 3.89 seconds
A triangle with vertices (2,-2), (-5,3) and (3,6) will be rotated 90 degrees clockwise around the origin and then reflected across the y-axis producing a triangle image. Which additional transformation will map the triangle back to it's original points? A rotation 270° counterclockwise around the origin B rotation 180° counterclockwise around the origin C reflection across the line y = –x D reflection across the line y = x
What is D) reflection across the line y = x.
Describe the intervals of increasing and intervals of decreasing for the function -x^2 + 10
What is increasing from (-infinity to 10) decreasing from (10 to infinity)
A building that is 54 feet high casts a shadow that is 72 feet long. What is the angle where the shadow meets the ground? *HINT*- use trig identities and draw a picture.
What is arcsin(54/72) = 60 degrees
Solve the following equation and identify all possible solutions: 8x^2 -4x + 5 = 0
What is 1 + - 3i / 4
Given: Triangle QSR and triangle TSR are right triangles, QS is congruent to TS Prove: Triangle QSR is congruent to triangle TSR *HINT*- draw it out! Statements: Reasons: 1. Triangle QSR and triangle TSR 1. are right triangles 2. 2. Given 3. 3. Reflexive property 4. Angle QRS is congruent to 4. All right angles are angle TSR congruent 5. 5. HL
What is Statements: Reasons: 2. QS is congruent to TS 1. Given 3. SR is congruent to SR 5. Triangle QSR is congruent to triangle TSR
Sketch a graph to demonstrate the following inequality: -b^2 + 8b - 10 > 0
What is U shaped graph with zeros at 1.55 and 6.45. Graph should be shaded between the two zeros.