Download MFM 2PI - U8 - D3 - Solving for an Unknown Angle

MFM 2PI ­ U8 ­ D3 ­ Solving for an Unknown Angle ­ complete
Unit 8: Trigonometry
Day 3: Solving for an Unknown Angle
Last class we...
- learned the steps to solve for an unknown side of a right-angled
triangle using the primary trig ratios
- used these steps to solve real-world problems
Today we will...
- learn the steps to solve for an unknown angle of a right-angled
triangle using the primary trig ratios
- use these steps to solve real-world problems
**Quiz next class!!**
MFM 2PI ­ U8 ­ D3 ­ Solving for an Unknown Angle ­ complete
Recap from last class
Steps for finding a missing side of a Right Triangle using Primary Trig Ratios
1. Identify your reference angle
2. Label your triangle using the reference angle
3. Decide what ratio to use (using the Have, Need, Use method)
4. Cross multiply
5. Isolate x
6. Conclude
Warm­Up: With your partner, complete the question on the board.
MFM 2PI ­ U8 ­ D3 ­ Solving for an Unknown Angle ­ complete
Solving for an Unknown Angle
Trig ratios can also be used to find the measures of angles of a right triangle that are not known.
Ex. 1 Use a calculator to find the measure of each angle A to the nearest degree.
a) cos A = 0.4067
b) sin A = 0.7777
c) tan A = 2.246
MFM 2PI ­ U8 ­ D3 ­ Solving for an Unknown Angle ­ complete
Steps for Solving for an Unknown Angle
1. Identify your reference angle
2. Label your triangle using the reference angle
3. Decide what ratio to use (using the Have, Need, Use f
method)
4. Inverse function
5. Conclude
MFM 2PI ­ U8 ­ D3 ­ Solving for an Unknown Angle ­ complete
Ex. 2: For the following triangles, identify the trig ratio to use, write the equation and solve it to one decimal place using the inverse trig buttons
on your calculator.
­1
­1
­1
tan
cos
sin
a)
Have:
35
Need:
x
Use:
12
Calculator:
tan
2nd
(35 12)
=
or
(35 12)
2nd
tan
=
Have:
b)
100
Need:
Use:
x
91
40
Have:
c)
x
50
Need:
Use:
MFM 2PI ­ U8 ­ D3 ­ Solving for an Unknown Angle ­ complete
Ex. 3 A storm caused a 13.5m hydro pole to lean over. The top of the pole is now 11.8m above the ground. Find the measure of the angle between the hydro pole and the ground, to the nearest degree.
Ex. 4 The Canadian Standards Association states that the angle between a ladder and the ground must be between 70 and 80 for safety. A 12m ladder is leaning against a building so that it reaches a height of 11.5m. Is this ladder positioned safely according to the Canadian Standards Association? Explain.
MFM 2PI ­ U8 ­ D3 ­ Solving for an Unknown Angle ­ complete
Practice Questions:
pg. 71 #2ace, 6, 8
pg. 80 #2a, 11, 13
QUIZ NEXT CLASS!!!