1. Explain the term trigonometry.

2. Identify the three trigonometric ratios that apply to right angle triangles.

3. Calculate values for the three trigonometric ratios that apply to right angled triangles.

Deals with the measurements of the sides and angles of triangles and their relationships with each other.

For right angled triangles there are six trigonometric ratios that apply.

We use the following three ratios in the main.

Sine Ɵ = opposite__ hypotenuse

Cosine Ɵ = adjacent__ hypotenuse

Tangent Ɵ = opposite adjacent

SOHCAHTOA.

Sine Ɵ = Opposite___ SOH Hypotenuse

Cosine Ɵ = Adjacent__ CAH Hypotenuse

Tangent Ɵ = Opposite_ TOA Adjacent

Find the unknown angles in the following triangle.

3m5m

4m

Ø

Since we know the length of each side we can use any of the three ratios to find Ɵ and Ø.

Sin Ɵ = _opposite__ = 3m = 0.6 hypotenuse 5m

Cos Ɵ = _adjacent__ = 4m = 0.8 hypotenuse 5m

Tan Ɵ = opposite = 3m = 0.75adjacent 4m

Ø

5m

4m

3m

To find Ɵ you should use your calculator.

Sin Ɵ = opposite = 3m = 0.6 hypotenuse 5m Sin Ɵ = 0.6 Ɵ = Sinˉ¹ 0.6 Ɵ = 36.87°

5m

4m

3m

Ø

Ø can be found from 180 - 90 - 36.87 = 53.13° This can be proved by trigonometry.

Sin Ø = _opposite__ = 4m = 0.8 Ø = 53.13° hypotenuse 5m

Cos Ø = _adjacent__ = 3m = 0.6 Ø = 53.13° hypotenuse 5m

Tan Ø = opposite = 4m = 1.33 Ø = 53.13°adjacent 3m

3m5m

4m

Ø

Ɵ = 36.87°

Ø = 53.13°

1. Explain the term trigonometry.

2. Identify the three trigonometric ratios that apply to right angle triangles.

3. Calculate values for the three trigonometric ratios that apply to right angled triangles.