Download Triangles on the Cartesian Plane

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.
Triangles on the Cartesian Plane
LG: I can determine the measure on an angle in standard
position on a Cartesian plane.
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
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
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
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 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
The terminal arm of an angle, Ө, in standard position passes through B(-5, 6).
a) Sketch a diagram for this angle in standard position.
b) Determine the length of OB.
c) Determine the value of Ө to the nearest whole degree.
Homework
• Complete back on handout
• Extra practice for quiz:
• Pg. 26 #1-5