Geometry and Trigonometric Functions: Practice Exercises

Here are various Exercises to accompany the section Geometry and Trigonometric Functions.  

The Geometry of Right Triangles

  1. Given the indicated measurements in a triangle labeled as follows:
    where C = p/2, determine all the remaining measurements.  Note: This picture should only be used to indicate the names of angles and their corresponding opposite sides; the actual measurements in the picture will be different from those in the Exercises.
    1. If we know that a = 5 in. and b = 3 in., compute approximate values for c, A, and B.
    2. If we know that b = 3 ft. and c = 7 ft., compute approximate values for a, A, and B.
    3. If we know that A = 0.8 radians and b = 3 m., compute approximate values for a, c, and B.

    Solution.

  2. Solve for the unknown measurement in each of the following pictures.  Note: This pictures are not drawn to scale; they simply intended to provide an applied context for the question.
    1. Find the height, h, (to the roofline) of the building: .
    2. Find how high, h , the kite is off the ground: .
    3. Find the angle, A, the 6 ft. ladder makes with the ground: (side view).

    Solution.

Two General Formulas for Triangles

  1. Given the indicated measurements in a triangle labeled as follows:
    determine all the remaining measurements.  Note: This picture should only be used to indicate the names of angles and their corresponding opposite sides; the actual measurements in the picture will be different from those in the Exercises.
    1. If we know that a = 5 ft., b = 3 ft., and c = 7 ft., compute approximate values for C, A, and B.
    2. If we know that a = 5 ft., b = 3 ft., and c = 9 ft., compute approximate values for C, A, and B.
    3. If we know that a = 80 mi., B = 0.25 radians, and C = 0.65 radians, compute approximate values for A, c, and b.
    4. If we know that a = 15 m., A = 0.4 radians, and c = 30 m., compute approximate values for C, B, and b.

    Solution.

  2. Solve for the unknown measurement in each of the following pictures.  Note: This pictures are not drawn to scale; they simply intended to provide an applied context for the question.
    1. Find the length, L, of the lake: (top view).
    2. Find the distance, d, to the top of the mountain: (side view)
    3. Use your answer to part b) to find the height, h, of the mountain: .

    Solution.

Go to Algebraic Functions.

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