Show:
8.1
The Geometric Mean
8.2
The Pythagorean Theorem
8.3
Special Right Triangles
8.4 Trigonometry
8.5 Applications of Trig
100
What is the geometric mean of 4 and 64?
16
100
The measure of the hypotenuse of a right triangle with a leg = 3, and the other leg = 4.
5
100
What type of 'special right triangle' is an isosceles right triangle?
45-45-90
100
The relationship between side lengths and angle measures within triangles.
What is Trigonometry?
200
What is the geometric mean of 3 and 27?
9
200
The measure of a leg of a right triangle with the other leg = 6, and the hypotenuse = 10
8
200
What is the length of the hypotenuse equal to in a 45-45-90 triangle?
The square root of 2 times the measure of the legs
200
SOH-CAH-TOA
What is a memory aid (mnemonic) of the Trig ratios SINe = (opp/hypo), COSine = (adj/hypo), and TANgent = (opp/adj)?
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
What is the geometric mean of 1 and 9?
3
300
What is the length of a leg if one leg equals 10 and the hypotenuse equals 26?
24
300
What is the measure of the HYPOTENUSE of a 30-60-90 right triangle?
2 times the measure of the short leg
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
What is the geometric mean of 6 and 18?
6 square roots of 3
400
What is the length of the hypotenuse if one leg equals 30 and the other leg equals 16
34
400
If the hypotenuse of a 45-45-90 triangle is 12, what is the measure of the two legs?
6 times the square root of 2
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
Find x for the given triangle.
6
500
What is the length of the hypotenuse if one leg equals 21 and the other leg equals 72?
75
500
If the length of the hypotenuse in a 30-60-90 triangle is 10, what are the lengths of the two legs?
Longer leg = 5 times the square root of 3 Shorter leg = 5
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)