2. Classifying Triangles By Angles Acute: all three angles are less than 90 ◦ Obtuse: one angle is greater than 90 ◦ Right: one angle measure is 90 ◦ By Sides Equilateral: all sides equal, all angles equal (60 ◦ ) Isosceles: two sides equal, two angles equal Scalene: no sides equal, no angles equal

3. Pythagorean Theorem a 2 + b 2 = c 2 This is the starting point of trigonometry. The hypotenuse “c” is always opposite the right angle. a c b

4. Triangles: Labelling Triangles

5. Trig Ratios SOH – CAH - TOA

6. Solving Right Triangles Pythagoras Finds the length of a side Given two other sides. Angle sum principle Finds the size of an angle Given the other two angles. Trig ratios Find the size of one acute angle Given two sides Find the length of a side Given an angle and one side.

7. Example What is the height of the tree? 37 o 8 m

8. Examples Calculate the measure of  A. 5 cm 12 cm C B A

9. Example An 8m ladder is leaning against a building. The distance from the foot of the ladder to the building is 2.5m. Find the measure of each acute angle in the triangle formed by the ladder, the building and the ground.

10. Examples Solve  ABC. Find lengths to the nearest tenth of a centimetre and angles to the nearest degree. 11 cmcm 13 cmcm C B A