8.1
The Geometric Mean
8.2
The Pythagorean Theorem
8.3
Special Right Triangles
8.4 Trigonometry
8.5 Applications of Trig
100
16 is between 4 and 64.
What is the Geometric Mean between 4 and 64?
100
The measure of the longest side of a right triangle with a leg = 3, and the other leg = 4.
What is 5?
100
One of 2 congruent triangles when a square is cut along its diagonal.
What is a 45-45 RIGHT triangle?
100
From the Greek, meaning "TRIANGLE MEASUREMENT" (based on properties and similarities of RIGHT triangles).
What is Trigonometry?
100
Determines the approximate height of a pole or a radio tower by measuring the length of the pole's shadow when one's height is the same length as one's shadow.
What is the METHOD of finding the height of a pole or tower, without climbing, or using similar triangles, the Pythagorean Theorem, or Trig ratios (SOHCAHTOA)?
200
9 is between 3 and 27.
What is the Geometric Mean between 3 and 27?
200
The measure of a leg of a right triangle with the other leg = 3, and the hypotenuse = 5
What is 4?
200
One of 2 congruent triangles formed when an equilateral/equiangular triangle is cut along one of its altitudes.
What is a 30-60 RIGHT triangle.
200
SOH-CAH-TOA
What is a memory aid (mnemonic) of the Trig ratios SINe, COSine, and TANgent?
200
The height of kite that Mary is flying on a 50-meter string that makes a 30-degree angle with the ground.
What is 25 feet (from height of kite = 50 times SINe 30-degrees) or { height = (50)(sin 30) }?
300
3 is between 1 and 9
What is the Geometric Mean between 1 and 9?
300
The measure of the hypotenuse of an ISOSCELES right triangle with each of the two legs = x.
What is x times the square root of 2, or x √2?
300
This longest side of a right triangle is TWICE or 2 times the measure of the short leg.
What is the measure of the HYPOTENUSE of a 30-60 right triangle?
300
The ratio of the Opposite side of an acute angle of a right triangle divided by the Hypotenuse.
What is the SINe (the Trig ratio) of the angle?
300
The measure of the height of a window with a 40 feet ladder leaning on it, making a 30-degree angle with the window's wall.
What is approximately 35 feet, or 40 times COSine 30 (from: COS 30 = wall height/40)?
400
The same number in the numerator and denominator of 2 ratios in a proportion.
What is the Geometric Mean between 2 numbers?
400
The measure of the 2 sides of a right triangle when long side is x times the √3 or (x) √3.
What is x (the measure of the short side), and 2x (the measure of the hypotenuse)?
400
The longest side of a right triangle is the measure of one of its legs times the square root of 2.
What is the measure of the hypotenuse of a 45-45 right triangle?
400
The ratio of the Adjacent side of an acute angle of a right triangle divided by the Hypotenuse.
What is the COSine (the Trig ratio) of the angle?
400
The measure of the angle of elevation of a trolley track that rises 40 feet vertically over a distance of 630 feet.
What is ≈ 3.6 (from TANgent of angle of elevation = 40/630)?
500
The square root of the product of 2 numbers.
What is the Geometric Mean between 2 numbers?
500
The measure of the side of a triangle with hypotenuse is 13 and the leg is 12.
What is 5, the measure of the other leg?
500
If (the longest side)2 of a triangle is the same as [(one of its side)2 + (the other side)2], THEN the triangle is a right triangle.
What is the CONVERSE of the Pythagorean Theorem?
500
The ratio of the Opposite side of an acute angle of a right triangle divided by the Adjacent side to the angle.
What is the TANgent (the Trig ratio) of the acute angle of triangle?
500
The acute angles of right Δ ABC with AC = 3 meters, BC = 4 meters, AB = 5 meters, that is needed by a tile-setter so he can cut tiles precisely for the hypotenuse-edge of the floor.
What is m ∠ B ≈ 37 {from tan B = 3/4, or cos B = 4/5, or sin B = 3/5} and m ∠ A ≈ 53 (from tan A = 4/5, cos A = 3/5, and sin A = 4/5)
M
e
n
u