Distance
Distance between
(2,1) and (2,7)
6
Slope of the line
y = 2x
2
In a right triangle, if the opposite side is 3 and the hypotenuse is 5, what is sin(θ)
o/h=3/5
Two triangles are similar. One has a side of 4 cm and the corresponding side of the other is 8 cm. What is the scale factor?
(8cm)/(4cm) = 2
You are painting a triangular wall mural. The triangle is 10 feet wide and 6 feet tall. How many square feet do you need to paint?
30 ft^2
Midpoint of line segment with endpoints
(4,2) and (6,10)
(5,3)
Name a point on the line
y = 3x-5
Any point that can be written as
(x,3x-5)
What trig ratio is equal to adjacent over hypotenuse?
cos(\theta)
Two similar rectangles have a scale factor of 3:1. The smaller rectangle is 5 cm wide. How wide is the larger one?
15 cm
A football field is 100 yards long and 53 yards wide. What is the total area of the field?
5300 square yards
Distance between
(1,3) and (6,-9)
13
Write the equation of a line in slope-intercept form that has a slope of 3 and passes through the point (1,2).
y = 3x + 2
A ladder leans against a wall. The ladder is 10 ft long and makes a 60° angle with the ground. How high up the wall does it reach?
10sin(60°)ft\approx8.66 ft
Triangle ABC is similar to Triangle DEF. AB = 6, BC = 9, and DE = 10. What is EF?
EF=15
You are filling a cylindrical water tank with a radius of 3 feet and a height of 8 feet. How many cubic feet of water does it hold?
72pi \approx 226.08 cubic feet
Distance between
(0,0) and (1,1)
sqrt(2)
What is the slope of a line perpendicular to
y=1/2x-6
-2
In a right triangle, the adjacent side is 7 and the hypotenuse is 25. What is cos(θ)?
a/h=7/25
Two similar triangles have a scale factor of 2:5. The area of the smaller triangle is 16 cm². What is the area of the larger triangle?
100 cm^2
A farmer wants to fence in an L-shaped field. The shape is made of two rectangles: one that is 20 m × 10 m and another attached piece that is 8 m × 5 m. What is the total area the farmer is fencing in?
200 + 40 = 240 m²
Partition segment into a ration of 1:3 with endpoints
(2,2) and (10,-10)
(4,-1) or (8,-7)
Write the equation of a line that passes through (-2, 1) and (4, -5) in point-slope form.
y-1=-(x+2)
A person standing 40 feet from the base of a tree looks up at a 35° angle of elevation to the top. How tall is the tree?
40tan(35°) ft \approx 28 ft
A building casts a 45-foot shadow at the same time a 6-foot person casts a 9-foot shadow. How tall is the building?
30 ft
A concrete company is pouring a foundation that is a rectangular slab 24 feet long, 18 feet wide, and 6 inches (0.5 ft) thick. Concrete costs $4 per cubic foot. How much will the concrete cost?
Volume = 24 × 18 × 0.5 = 216 ft³; Cost = 216 × $4 = $864