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
This rotation results in the same final location as rotating a point 270 degrees counter-clockwise
What is 90 degrees clockwise
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)
A trapezoid has bases of lengths 5 and 4, and an area of 9. What is the height of the trapezoid?
What is a height of 2?
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. How deep is the water beneath the boat?
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
Which of the following types of angles are always congruent? Corresponding, Alternate exterior, Vertical, Same side interior, Same side exterior, Alternate interior, Linear pair
What are Corresponding, Same side exterior Vertical, Alternate exterior, and Alternate interior angles?
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 path of a ball shot into the air is modeled by the equation f(t) = -(t-5.5)2 + 36 where t is time in seconds and f(t) is height (in feet) of the ball. How many seconds will it take for the ball to return to the ground?
What is 11.5 seconds
This ray splits an angle into two separate, congruent angles.
What is an angle bisector?
What is the axis of symmetry of the equation y=3x2 + 9x + 4
What is x = -3/2
The top of a 12-foot ladder is placed 10 feet high on the side of a building. How far away from the building is the base of the ladder, to the nearest tenth of a foot?
What is 6.6 feet?
Solve the following equation and identify all possible solutions: 8x^2 -4x + 5 = 0
What is 1 + - 3i / 4
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.
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.
Cassie is worried about her upcoming exams. She predicts that there is a 95 percent chance she will pass her Math 2 exam, and a 70 percent chance she will pass her World History Exam. What is the probability Cassie passes both her exams?
What is 66.5%?