# Triangles on the Cartesian Plane - Ms Beaubien's Classroom Warm-Up: Applications of Right Triangles At ground level, the angle of elevation to the top of a building is 78. 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 90 Obtuse Angle = Greater than 90 (but less than 180) Reflex Angle = greater than 180

Supplementary Angles = two angles that add to 180 two right angles, or One acute and one obtuse angle obtuse acute Angle Conventions On a Cartesian plane (or co-ordinate axes) we position angles like this: Terminal arm

Positive angles are read counter-clockwise Rotation Angle Initial arm 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

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

r EXAMPLE 1 Acute Angles in Standard Position For the angle in standard position with a terminal arm passing through P(5, 2): a) Find the length of r

b) Determine the measure of each trig ratio. Round your answers to four decimal places. c) Determine the measure of 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, , in standard position. Calculate to the nearest whole degree.

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