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SohCahToa Project

Detail 4

Theta

  • θ is a variable that represent the angle.

Real World Problem

Joe and Ben went jogging 5 miles north and then 3 miles west. How far did they travel from their starting point?

Opposite is always across from theta.

x

5

a2 + b2 = c2

3^2 + 5^2 = c2

9 + 25 = 34

34

opposite

hypotenuse

3

Leg

x = 17 miles

adjacent

  • The legs are the two shortest side of the triangle.
  • The legs of the right triangle are perpendicular to each other.

3 Basic Ratios

Sin (soh) : Opposite/Hypotenuse

Cos (cah) : Adjacent/Hypotenuse

Tan (toa) : opposite/Hypotenuse

Detail 1

Pythagorean Theorem

The sum of the areas of the two on the legs (a and b) equals the area of the hypotenuse.

a2 + b2 = c2

Detail 2

  • c is the longest side of the triangle.
  • a and b are the other two sides.

a2 + b2 = c2

3^2 + 4^2 = 5^2

9 + 16 = 25

25 = 25

Example:

3

5

4

Detail 3

trigonometric is a 3 side angles.

  • Adjacent Leg : Adjacent is always next to the angle.
  • Opposite Leg: Always across from the angle.
  • Hypotenuse: Longest side of a right triangle.

example:

by : Tram Nguyen

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