Similar Triangles & Trig
What are the only three theorems we can use to argue two triangles being similar?
What is AA, SSS, SAS
What are the zeros of the quadratic equation below?
y=(x-a)(x+b)
In factored form, zeros are the opposite sign of the values in the parentheses
x=a
x=-b
State the three rigid transformations
translation, rotation, dilation
NOTE: dilation is a nonrigid transformation
A cone and a cylinder have the same base circle and the same height. The cone has a volume of 4 fluid ounces. What is the volume of the cylinder?
The cylinder is 3 times the volume of the cone if they have the same base and height.
4*3=12 fluid ounces
Benji has a basket with green limes, yellow lemons, yellow bananas, and orange oranges.
He picks a yellow fruit. What would be the complement of that?
What is he picked a lime or an orange
In triangle ABC with right angle B, sin(A)=0.43 What other trig ratio for the triangle equals 0.43?
sin(A)=cos(90-A)
sin(A)=cos(C)
cos(C)=0.43
what is the vertex of the quadratic equation below?
y=7(x-m)2+4
(m,4)
Circle A has radius 5 and is dilated to achieve Circle B with radius 19. What is the scale factor?
new/old
19/5
A right cone and an oblique cone have the same base radius and heights. The right cone has a volume of 7in3. What is the volume of the oblique cone?
Cavalieri's principle says as long as the base area and height are the same, the volumes are the same.
V=7in3
"And" means multiply.
1/2*1/6=1/12
DRAW a picture!
In triangle ABC with right angle B, AB is 20, AC is 29, and BC is 21. What is tan(A)?
tan(A)=opposite /adjacent
21/20
You are designing a bedroom for an apartment. Regulations state the area of the bedroom must be 132 square feet. The client has requested the bedroom is 4 feet wider than it is long. Write an equation in terms of the length, l, of the bedroom's area.
A = Lw
132=l(l+4)
Which is the only transformation that changes orientation?
How can you check if orientation has changed between two figures (ex: ABC and A'B'C')
Only reflections change orientation
To check orientation, start at A in figure ABC and go around the figure clockwise noting which vertex you get to next. Do the same in A'B'C' from A'. If the order of letters is different, a reflection has occurred.
A sphere has a diameter of 24 inches. What is the volume? Write your answer in terms of π
V=4/3 π r3
V=4/3 π (12)3
V=2304 π inches3
Priya is rolling a six-sided number cube. She rolls it 4 times and writes the result for each.
Trish is picking marbles from a bag with 3 red and 2 blue marbles. She pulls three at once.
Carlos is picking cards from a deck. He picks one, returns it and shuffles, then pulls a second.
Which students are completing INDEPENDENT probability experiments?
Priya and Carlos
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.
The flight of a rocket launched in the air can be modeled by the function f(t) = 2t2 -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? Round to the nearest hundredth if necessary
What is 3.89 seconds
A triangle with vertices (2,-2), (-6,3) and (10,6) is dilated by a scale factor of 1/2 from the origin. What are the new ordered pairs?
When dilating from the origin, multiply each ordered pair value by the scale factor.
(1,-1) (-3,1.5) and (5,3)
Solve for the positive value x, in terms of π :
π x2+b=k
π x2=k-b
x2=(k-b)/π
x=√ [(k-b)/π ]
There's a 20% chance you have dimples, and a 25% chance you have a cleft chin. If these are independent, what is the probability you have dimples OR a cleft chin?
P(A or B)=P(A)+P(B)-P(A and B)
Since independent, P(A and B)= 0.20*0.25=0.05
0.20+0.25-0.05=0.40 or 40% chance
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 sin-1(54/72) = 60 degrees
write a quadratic equation with no real solution
Any equation which would require you to square root a negative. For example,
x2=-8
A circle has center (5,-9) and radius 6. Write the equation of the circle
(x-5)2+(y+9)2=36
A cylinder with a volume of 5 units3 has it's lengths scaled up by a factor of 2. What is the new volume?
Volume's change is always cubed compared to length scale factor.
5*23=5*8=40 units3
At a local vet with 325 pet clients, there is a 40% chance a randomly selected patient is a dog. 65 of the vet's pet clients are obese dogs. What is the probability a dog client is obese?
P(A given B)=P(A and B)/P(B)
P(dog and obese)=65/325=0.2
P(dog)=0.4
P(obese given dog)=0.2/0.4=50%