math
What is "sin" equal to?
Opposite / Hypotenuse
Angle of elevation is looking... (up or down)?
What is "cos" equal to?
Adjacent / Hypotenuse
Angle of depression is looking... (up or down)?
What is "tan" equal to?
Opposite / Adjacent
Find sin(8).
sin(8) = 0.14
Type it in your calculator in DEG mode!
Find cos(76).
cos(76) = 0.24
Use your calculator in DEG mode!
Find tan(82).
tan(82) = 7.12
Use your calculator in DEG mode!
Find the geometric mean between 2 and 50.
√ (2*50) = 10
square root of 2 times 50
Find the geometric mean between 7 and 11.
√(7*11) = 8.77
square root of 7 times 11
What is the Pythagorean Theorem?
a2 + b2 = c2
What is the equation for finding geometric mean?
square root of two multiplied numbers
geometric mean = √(x * y)
What is the hypotenuse of a right triangle with side lengths 2 and 2√3?
hypotenuse length = 4
(use Pythagorean Theorem! a2 + b2 = c2)
What is the hypotenuse length of a right triangle with side lengths 3 and √27 ?
hypotenuse length = 6
(use Pythagorean Theorem! a2 + b2 = c2)
What is the hypotenuse of a right triangle with side lengths 7 and 7√3 ?
hypotenuse length = 14
(use Pythagorean Theorem! a2 + b2 = c2)
Solve for x:
sin(32) = x / 10
x = 5.299 or 5.30
[10 * sin(32) = x ]
Solve for x:
cos(45) = x / 21
x = 14.85
[21 * cos(45) = x]
Solve for x:
tan (89) = x / 18
x = 1031.22
[18 * tan(89) = x ]
Angle = 18 degrees
Opposite side length = 12 feet
Hypotenuse = ?
Which trig ratio do you use to solve for the hypotenuse?
trig ratio = sine
Angle = 42 degrees
Hypotenuse = 9.5
Adjacent side length = ?
What trig ratio do you use to solve for the adjacent side?
trig ratio = cosine
Angle = 30 degrees
Opposite side length = 4
Hypotenuse side length = 5
Adjacent side length = 3
What is the equation to solve for tangent?
tan(30) = 4/3
Angle = 45 degrees
Adjacent side length = 2 meters
What is the length of the opposite side?
tan(45) = x / 2
2*tan(45) = x
x = 2
An internet cable from an electrical tower forms a 65 degree angle with the ground. The cable is 17 feet from the base of the tower.
How tall is the tower?
tan(65) = x/17
17*tan(65) = x
x = 36.46 feet
A boat locates a treasure chest at an angle of depression equal to 12 degrees. If a diver sinks 40 meters to the ocean floor, how far does the diver have to swim to reach the treasure chest?
tan(12) = 40/x
x = 40/tan(12)
x = 188.19 meters (horizontal distance to swim)
A turtle is swimming & looks up 52 degrees to see a lighthouse. The lighthouse is 40 meters away on the beach. How tall is the lighthouse?
tan(52) = x/40
40 * tan(52) = x
x = 51.198 or 51.20 meters tall