Solving Word Problems involving Oblique Triangles

Solving Word Problems involving Oblique Triangles

I can illustrate Law of Sines

1.

I can illustrate Law of Cosines

2.

I can solve word problems involving oblique triangles

3.

​Learning targets

• In what other fields can Trigonometry be used?

• How can the knowledge of Trigonometry be applied in solving real-life problems?

Essential Questions:

Multiple Choice

Which of the following can be used to solve for the missing side?

• Law of Sines

• Law of Cosines

• SOH-CAH-TOA

• Pythagorean Theorem

Multiple Select

Which of the following can be used to solve for m∠Y?

Fill in the Blanks

What measure indicates the true bearing of point S from point C in the figure?

Fill in the Blanks

What measure indicates the conventional bearing of point S from point C in the figure?

Draw

Problem 1:
(Read, analyze, & visualize the problem)

A large helium balloon is tethered to the ground by two taut lines. One line is 100 feet long and makes an 80⁰ angle with the ground, while the second line makes a 40⁰ angle with the ground.
a. How long is the second line?

b. How far apart are the two tethers

Fill in the Blanks

A large helium balloon is tethered to the ground by two taut lines. One line is 100 feet long and makes an 80⁰ angle with the ground, while the second line makes a 40⁰ angle with the ground.
a. How long is the second line?

Fill in the Blanks

A large helium balloon is tethered to the ground by two taut lines. One line is 100 feet long and makes an 80⁰ angle with the ground, while the second line makes a 40⁰ angle with the ground.
b. How far apart are the two tethers?

Draw

Problem 2: PAIR WORK
(Read, analyze, & visualize the problem)

A ship leaves a port and sails for 47 nautical miles on a course of 78 degrees. Then the ship changes its course to 158 degrees and sails for 96 nautical miles.

a. What is the distance of the ship from a port

b. What is the bearing from the port to the ship?

Fill in the Blanks

A ship leaves a port and sails for 72 nautical miles on a course of 78 degrees. Then the ship changes its course to 158 degrees and sails for 96 nautical miles.

a. What is the distance of the ship from the port?

Fill in the Blanks

A ship leaves a port and sails for 72 nautical miles on a course of 78 degrees. Then the ship changes its course to 158 degrees and sails for 96 nautical miles.

b. What is the true bearing from the port to the ship?

Open Ended

In what cases of oblique triangles do we need the use of Law of Sines and Cosines?

Match

Match the given conditions of an oblique triangle with the corresponding law.

• SSS

• SSA

• SAS

• SAA

• ASA

Law of Cosines

Law of Sines (Ambiguous Case)

Law of Cosines

Law of Sines

Law of SInei

• Law of Cosines

• Law of Sines (Ambiguous Case)

• Law of Cosines

• Law of Sines

• Law of SInei

Open Ended

• In what other fields can Trigonometry be used?

• How can the knowledge of Trigonometry be applied in solving real-life problems?

Poll

How did you find our lesson?

• 4
  I understand the lesson and I can teach it to others.

• 3
  I understand the lesson and I can do it on my own.

• 2
  I understand the lesson but I need guidance in some parts.

• 1
  I did not understand the lesson, and I need help in most parts.