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
23 December, 05:31
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.
Assume that m∠A is known, then m∠B = 90° - m∠A.
Also, assume that b is known.
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.
Because a and c are known,
sin A = a/c
A = sin⁻¹ (a/c), which can be determined from the calculator.
Know the Answer?
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» 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