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23 December, 05:13

In addition to the trigonometric ratios, what other methods can be used to solve a right triangle? Give situations for when you might want to use them

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  1. 23 December, 05:31
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    Consider the right triangle shown below.

    We shall discuss two methods for solving the right triangle.

    Method 1. Use of trigonometric ratios

    To use trigonometric ratios requires that either m∠A or m∠B is known and that one of the sides a, b, or c is known.

    Example:

    Assume that m∠A is known, then m∠B = 90° - m∠A.

    Also, assume that b is known.

    By definition,

    tan A = a/b = > a = b*tan A

    cos A = b/c = > c = b/cos A, or

    sin A = a/c = > c = a/sin A

    Method 2. Algebraic method

    When neither m∠A nor m∠B is known, then it is necessary to know the values of two sides: (a and b), (a and c), or (b and c).

    The Pythagorean theorem states that

    a² + b² = c²

    (a) If a and b are known, then

    c = √ (a² + b²)

    (b) If a and c are known, then

    b = √ (c² - a²)

    (c) If b and c are known, then

    a = √ (c² - b²)

    Once all sides are known, trigonometric ratios can be used t determine m∠A and m∠B.

    Example:

    Because a and c are known,

    sin A = a/c

    A = sin⁻¹ (a/c), which can be determined from the calculator.
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