Question

LAW OF SINES & COSINES Scavenger Hunt The trumpet, clarinet, and flute sections formed a triangle during marching band practice. The clarinet line made a 34° angle with the flute line. The flute line made a 107° angle with the trumpet line. If the flute line was 27 feet long, find the length of the clarinet line. © Gina Wilson (All Things Algebra®, LLC),

Answer 1

Sure, The length of the clarinet line is approximately 15.79 feet.

Here's how I found it:

1. Identified the relevant information:

- The angles of the triangle: 34° for the clarinet-flute angle, 107° for the flute-trumpet angle.

- The length of the flute line: 27 feet.

2. Applied the Law of Cosines:

- We know two side lengths (flute and clarinet) and the angle measure between them (clarinet-flute angle).

- We can use the Law of Cosines to solve for the unknown side length (clarinet line).

3. Formulated the equation:

a^2 = b^2 + c^2 - 2bc * cos(A)

- where:

- a is the clarinet line (unknown)

- b is the flute line (27 feet)

- c is the trumpet line (unknown)

- A is the clarinet-flute angle (34°)

4. Solved for the clarinet line:

- Plugged in the known values and solved for a.

- a ≈ 15.79 feet