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.