Oblique TrianglesPart II

Learning Goal: I can solve for a missing side or angle in a non-right triangle using cosine law

Recall: Sine Law

• The formula: = = • When do we use it? – Solving for missing side or angle in non-right

triangle• What do we need to use sine law?– Matching side and angle

Matching side and angle

Cosine Law• The formula: • When do we use it?

– Solving for missing side or angle in non-right triangle (when we don’t have a matching side and angle)

• What do we need to use cosine law?– All three sides OR two sides and the enclosed angle

We can solve for the third side

We can solve for any angle

Example 1 – solving for a side• Label the sides of the

triangle a, b, and c• Calculate the missing side

using cosine law

73⁰

2.3 km

1.9km

?C

A

B

Example 2 – solving for an angle• Label the sides of the triangle

x, y, and z• Write cosine law for this

triangle and calculate angle X3.3 cm

3.8 cm

2.7 cm

Y

X Z

Homework

• Pg. 38-39 # 2,3,7,8

Warm-Up: Cosine Law• Label the sides and write

triangle• Write cosine law to solve

for angle M

500 ft650 ft

750 ft

M

L N

Applications of Cosine Law

Learning Goal: I can solve problems based on realistic situations using cosine law

Example 1 – NavigationTwo planes are heading toward a control tower. From the tower, one plane is 86 km due North. The second plane is 146 km away at an angle of 53⁰ W of N. How far apart are the two planes?

Example 2 - Race CourseA bike race follows a triangular route. It begins in the town Shaw. Bikers must travel 17km from Shaw to Bronston, 12km from Bronston to Gage, then 19 km back to Shaw. At what angle must the biker turn to continue on the second leg of the race?

Homework

• Pg. 39 # 10, 11, 13, 15, 18