Download Sine Law

MPM2D
Unit #8 - Lesson #1
8.1/8.2 - The Sine Law
Recall:
 We can only use PRIMARY TRIGONOMETRIC RATIOS when working with ________
triangles.
 Now we will be working with non-right triangles, also known as ____________ triangles.
GOAL: Explore the relationship between each side in an acute triangle and the sine of
its opposite angle.
Discovering the Sine Law:
Steps
1. Start with acute ΔABC.
2. Since the primary trig ratios are only
used for right triangles, draw a
________________ ____________, AD,
from A to BC to form ____ right triangles,
Δ ABD and Δ ACD
3. Write equations for the SINES of <B and
<C in the 2 right triangles.
4. Isolate side AD in both equations from
step 3.
5. Set the expressions for AD _______ to
one another.
6. Write each side of the equation as a ratio
with information about only ONE triangle.
(Bring everything about “B” together and
everything about “C” together)
MPM2D
Unit #8 - Lesson #1
7. Divide Δ ABC differently so that we can
use < A. Draw height BE from B to AC to
create another 2 right triangles: Δ ABE and
Δ CBE.
8. Write equations for the SINES of <A and
<C in the 2 right triangles.
9. Isolate side BE in both equations from
step 8.
10. Set the expressions for BE _______ to
one another.
11. Write each side of the equation as a
ratio with information about only ONE
triangle. (Bring everything about “A”
together and everything about “C” together)
12. Write a final statement comparing all 3
ratios. This is the _______ _______.
 Sine Law  in any _________ triangle, you can use the following to calculate unknown
_______ lengths and ________ measures:
MPM2D
Unit #8 - Lesson #1
GOAL: Use the sine law to calculate unknown side lengths and angle measures in acute
triangles.
 To use the SINE LAW to determine a side length of angle measure, use these steps:
o
Determine the ratio of the sine of a __________ angle measure and a
_________ side length.
o
Create an ______________________ ratio using either:
 The ____________ side length and the measure of its KNOWN opposite
angle
OR
 The sine of an ____________ angle measure and the KNOWN length of
its opposite side.
o
__________ the ratios you created, and SOLVE for the unknown value.
Example: Determine the length of AC to the nearest metre.
Example: In Δ DST, ∠ D = 47°, d = 78 cm, and s =106 cm. Determine the measure of ∠S to the
nearest degree.
MPM2D
Unit #8 - Lesson #1
Example: Determine the indicated angle measures for Δ QRS.
You Try!
Sine Law
TWO known sides
and the angle that is
_________ one of
these sides
TWO known angles
and ANY one
_______
EXIT SLIP: Solve for “c” using the Sine Law.
Homework: pg. 427 #2, pg. 433 - 434, # 2, 3abcf, 5, 6