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Step-by-Step Guidance for Trigonometry Test 2 Review (Sections 5.5-5.8)

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Q49. Solve the right triangle given: ,

Background

Topic: Solving Right Triangles

This question tests your ability to use trigonometric ratios and the Pythagorean theorem to solve for unknown sides and angles in a right triangle.

right triangle labeled A, B, C, a, b, c

Key Terms and Formulas:

  • Right triangle: One angle is .

  • Pythagorean theorem:

  • Sine:

  • Cosine:

  • Sum of angles: (since )

Step-by-Step Guidance

  1. Calculate angle using the fact that the sum of the two non-right angles in a right triangle is :

  2. Use the sine ratio to solve for side : Rearrange to get

  3. Use the cosine ratio to solve for side : Rearrange to get

  4. Check your calculations for and using the Pythagorean theorem to ensure .

Try solving on your own before revealing the answer!

Final Answer: B = 31.4°, a = 46.2, b = 28.2

We used the angle sum property and trigonometric ratios to solve for the unknown sides and angle.

Q57. Find the bearing from O to B (see diagram).

Background

Topic: Bearings and Navigation

This question tests your understanding of bearings, which are used in navigation to describe direction relative to north or south.

bearing diagram with points O, A, B, C, D

Key Terms and Formulas:

  • Bearing: The direction from one point to another, measured in degrees from north or south.

  • Standard notation: Bearings are written as N/S followed by the angle and then E/W (e.g., N 41° W).

Step-by-Step Guidance

  1. Identify the location of point B relative to O using the diagram.

  2. Determine the angle between the north-south axis and the line OB.

  3. Express the bearing in the standard format (N/S, angle, E/W).

Try solving on your own before revealing the answer!

Final Answer: N 41° W

The bearing is measured from north towards west, based on the diagram and angle provided.

Q58. Find the bearing from O to D (see diagram).

Background

Topic: Bearings and Navigation

This question tests your ability to interpret bearings using a navigation diagram.

bearing diagram with points O, A, B, C, D

Key Terms and Formulas:

  • Bearing: Direction from one point to another, measured in degrees from north or south.

  • Standard notation: N/S, angle, E/W.

Step-by-Step Guidance

  1. Locate point D relative to O using the diagram.

  2. Find the angle between the north-south axis and the line OD.

  3. Write the bearing in the standard format (N/S, angle, E/W).

Try solving on your own before revealing the answer!

Final Answer: S 51° E

The bearing is measured from south towards east, based on the diagram and angle provided.

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