Warm-Up: Applications of Right Triangles At ground level, the angle of elevation to the top of a building is 78⁰. If the measurement is taken 40m from the base of the building, determine the height of the building.

Lesson 3:Triangles on the Cartesian Plane LG: I can determine the measure of an angle in standard position on a Cartesian plane. I can determine the values of the sine, cosine and tangent of obtuse angles.

Angle Terms Acute Angle = less than 90⁰ Obtuse Angle = Greater than 90⁰ (but less than 180⁰) Reflex Angle = greater than 180⁰ Supplementary Angles = two angles that add to 180⁰ two right angles, or One acute and one obtuse angle acute obtuse

Angle Conventions On a Cartesian plane (or co-ordinate axes) we position angles like this: Angles are said to be in standard position when the vertex is at the origin (0,0) and the initial arm is located on the positive x-axis Initial arm Terminal arm Rotation Angle Positive angles are read counter-clockwise

Calculator Practice Determine the sine, cosine and tangent for each angle. 115o b) 100o Is each trigonometric ratio positive or negative? Use a calculator to verify. sin98o b) tan134o Determine the measure of angle R for the cosine ratio -0.75.

Triangles on a Cartesian Plane Given the point (x, y), we know 2 side lengths of the right triangle Pythagorean theorem could be used to solve for the hypotenuse (r) Knowing all three sides of the triangle, we can use any primary trig ratio (sin, cos, or tan) to determine the measure of angle Ө r The hypotenuse is also called r for the radius of the circle that could be formed by extending the angle of rotation

EXAMPLE 1 Acute Angles in Standard Position For the angle in standard position with a terminal arm passing through P(5, 2): Find the length of r Determine the measure of each trig ratio. Round your answers to four decimal places. Determine the measure of Ө to the nearest whole angle.

EXAMPLE 2 Obtuse Angles in Standard Position The point P(– 3, 7) lies on the terminal arm of an angle, ɵ, in standard position. Calculate ɵ to the nearest whole degree.

Practice Pg. 23 #1, 2, 4-7