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 triangle is an isosceles triangle?
45-45-90
100
What type of triangles do trigonometric ratios involve?
Right triangles
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
What is a memory aid (mnemonic) of the Trig ratios SINe, COSine, and TANgent?
SohCahToa
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
Use a special right triangle to express the trigonometric ratio as a fraction sin 30
1/2
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 two positive numbers?
The square root of the product of the two numbers.
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
Use a special right triangle to express the trigonometric ratio as a fraction. tan45
1
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)