MPM2D
Unit #8 - Lesson #3
8.2/8.4 - Applications of the Sine Law and the Cosine Law
Recall:
 We can only use the SINE LAW and COSINE LAW when solving for an unknown
side length or an unknown angle measure in an ________________ triangle.

Sine Law  states that, for any acute Δ ABC, the following holds true:
o
We can apply the Sine Law in 2 possible scenarios:
 If we know TWO side lengths and ONE angle that is _____________ one
of the given sides
OR
 If we know TWO angles and _______ ONE side.

Cosine Law  states that, for any acute Δ ABC, the following 3 equations hold true:
o
We can apply the Cosine Law in 2 possible scenarios:
 If we know TWO side lengths and the ONE angle that is _____________
the two given sides.
OR
 If we know _______ THREE side lengths.
GOALS:
 Use the sine law to calculate unknown side lengths and angle measures in acute
triangles.
 Use the cosine law to calculate unknown side lengths and angle measures in acute
triangles.
 Apply the sine law and cosine law to acute triangle word problems.
 Draw and label acute triangles given the information provided.
 Identify which law is to be used in order to solve a problem using the information given.
MPM2D
Unit #8 - Lesson #3
Example: A group of students are going on a trip to an undeveloped country to aid in building a
new school for a low-income community. The roof of the new school must be built to exact
specifications so that solar panels can be installed. Solar panels are devices that use sunlight to
generate and supply electricity to lower the use of other electronic devices. The long rafters at
the front of the school must be inclined at an angle of 26º to the horizontal beam. The short
rafters at the back of the school must be inclined at an angle of 66º. The house is 15.3 m wide.
Determine the length of the long rafters to two decimals.
o
Draw and Label the Triangle Described
o
What Law Should be Used Based on the Information Provided? __________ _________
o
What Other Piece of Information Do We Need to Know in Order to Use This Law? _____
o
Determine the Missing Angle
o
Determine the Missing Length Indicated
o
Final Answer:
MPM2D
Unit #8 - Lesson #3
Example: The posts of a hockey net are 1.8 m apart. A player tries to score a goal by shooting
the puck along the ice from a point that is 4.3 m from one goalpost and 4.0 m from the other
goalpost. Determine the measure of the angle that the puck makes with both goalposts (to
the nearest degree).
You Try!
Bringing it All Together: To successfully solve an acute triangle word problem, we have to be
able to know WHEN we are supposed to use the Sine Law and the Cosine Law.
- 2 ______
______
Law
- Any 1 _____
- 2 ______
- 1 Opposite __________
Solving Acute
Triangles
- All 3 _________
________
Law
- 2 ________
- 1 _______ Between
EXIT SLIP: A 4m flag pole is on a tilt. A 4.17m wire is attached to the top and anchored in the
ground, making a 68° angle with the ground. What angle does the pole make with the ground?
Homework: pg. 434, # 7 - 11, 13, pg. 444 - 445, # 7, 9, 11 – 13, pg. 450, #2