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Warm-Up: Applications of R ight Triangles

Warm-Up: Applications of R ight 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.

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Warm-Up: Applications of R ight Triangles

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  1. 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.

  2. Triangles on the Cartesian Plane LG: I can determine the measure on an angle in standard position on a Cartesian plane.

  3. 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

  4. 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 Terminal arm Positive angles are read counter-clockwise Rotation Angle Initial arm

  5. 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

  6. 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.

  7. 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.

  8. 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 Өto the nearest whole degree.

  9. Homework • Complete back on handout • Extra practice for quiz: • Pg. 26 #1-5

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