Curriculum Outcomes
Geometry: Develop spatial sense. 2. Demonstrate an understanding of the Pythagorean theorem by:
4. Demonstrate an understanding of primary trigonometric ratios (sine, cosine, tangent) by:
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Things You Need to Know
- Trigonometry is the branch of mathematics that deals with angle measures and side lengths of triangles. In Math 10-3, we only deal with right triangle trigonometry.
- Right triangles are triangles with a 90° angle in them.
- The hypotenuse in a right triangle is the side that is opposite the right angle.
- For any triangle, the angles inside the triangle add up to 180°.
- If we already know two of the angles in a triangle, we can use this rule to find the missing angle.
- When we label triangles, angles are in capital letters and sides are lowercase letters.
- The letter we use for the side length is the lowercase version of the letter used for the opposite angle.
- The Pythagorean Theorem states that in a right triangle with sides a, b, c (c is the hypotenuse), the following equation is true:
- a² + b² = c²
- Remember: a² means a x a. To "undo" this, you need to take the square root (√ ).
- You can use the Pythagorean Theorem to find the length of a missing side if you're given 2 sides already.
- In right triangles only (triangles with a 90° angle), the following trigonometric ratios can be used to find missing angle measures and side lengths:
- sin (angle) = opposite / hypotenuse (the hypotenuse is the side length opposite the 90° angle)
- cos (angle) = adjacent / hypotenuse
- tan (angle) = opposite / adjacent
- These can be remembered using: SOHCAHTOA.
- The trigonometric ratios are used when we either know:
- 1 angle and 1 side (to help us find another side)
- 2 sides (to help us find an angle)
- In this case, we would need to use the "inverse" ratio to "undo" the trig function.
- "Solving" a triangle means finding ALL the angle measures and side lengths.
- Side lengths can be found in two ways:
- If you have two sides already, you can use Pythagoras' theorem ( a² + b² = c², where c is the hypotenuse)
- If you have one side and an angle, you can use a trigonometric ratio.
- Angle measures can be found in two ways:
- If you have two angles, use the fact that all 3 angles in a triangle add up to 180°.
- If you only know the 90° angle, set up a trigonometric ratio and use inverse ratio to find an angle.
- Side lengths can be found in two ways:
- Angle of elevation is the angle between the horizontal and the line of sight upwards.
- Angle of depression is the angle between the horizontal and the line of sight downwards.
Interactive Activities
Sample Problems
Class Notes