Answer:
To determine which trigonometric function to use in a triangle, you need to identify what sides and angles are given, and what you are trying to find. The three primary trigonometric functions are sine (sin), cosine (cos), and tangent (tan), which relate the ratios of the sides of a right triangle to its angles.
To determine which trigonometric function to use, you can use the acronym SOH-CAH-TOA, which stands for:
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
Let's take an example:
Question: In a right triangle ABC, where angle B is the right angle, the length of the hypotenuse is 10 cm, and the length of the adjacent side to angle A is 6 cm. What is the value of the sine of angle A?
Solution: We are given the hypotenuse and the adjacent side to angle A, and we want to find the sine of angle A. Looking at the SOH-CAH-TOA acronym, we see that sine involves the ratio of the opposite side to the hypotenuse. In this case, the opposite side to angle A is not given, but we can use the Pythagorean theorem to find it:
a² + b² = c², where a and b are the legs of the right triangle and c is the hypotenuse.
In our triangle, we have:
a² + 6² = 10²
a² + 36 = 100
a² = 64
a = 8
Now that we know the length of the opposite side to angle A is 8 cm, we can use the sine function:
sin(A) = Opposite / Hypotenuse = 8 / 10 = 0.8
So, the value of the sine of angle A is 0.8.
In summary, to determine which trigonometric function to use, you need to identify what sides and angles are given, and what you are trying to find. You can then use the SOH-CAH-TOA acronym to match the given sides with the appropriate function, and use the Pythagorean theorem and other trigonometric identities to find any missing sides or angles.
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