To find an angle where you have the opposite and adjacent which formula do you use? Sine, Cosine, Tan? and how do you find the inverse?
as an example make a right-angled triangle ABC with AB=5, BC=4 and AC=3
(notice 3^2 + 4^2 = 5^2)
relative to angle B, AC is the opposite, and BC is the adjacent, and AB is the hypotenuse.
the ratio AB/BC = opposite/adjacent is called the tangent of an angle.
in this case tangent B = 3/4 = .75
to get angle B depends on your calculuator.
I have a "Sharp" in front of me, and there is a 2ndF key at the top left
so to get my angle I press
2ndF
tan
.75
=
and I get 36.87º
to get angle A, you simple take the difference between that angle and 90º, since angle C = 90
to find the tangent of the angle, press
tan
36.87
=
you should get very close to .75,
(we won't get .75 itself, since we rounded off our previous result)
google 'trig ratios' and you should get the other two definitions
also look up SOHCAHTOA
When you have the opposite and adjacent sides of a right triangle and want to find the angle, you should use the tangent function. Tangent is defined as the ratio of the opposite side to the adjacent side.
To find the inverse of the tangent function, you need to use the arctangent or inverse tangent function. This will give you the angle corresponding to a specific tangent value.
So to summarize:
- Use the tangent function to find the angle when you have the opposite and adjacent sides.
- Use the arctangent or inverse tangent function to find the angle when you know the tangent value.
To find an angle when you have the opposite and adjacent sides of a right triangle, you can use the Tangent (Tan) function. The formula for tangent is defined as the opposite divided by the adjacent side:
Tangent (Tan) = Opposite / Adjacent
To find the inverse of the tangent function, which will allow you to find the angle, you use the inverse function called "arctangent" or "atan." Think of it as the opposite operation that "undoes" the effect of the tangent. The inverse of the tangent is usually denoted as "tan⁻¹" or "arctan."
To find the angle theta, you would use the following formula:
θ = arctan(Opposite / Adjacent)
Here's an example to illustrate the process:
Let's say you have a triangle where the length of the opposite side is 5 units, and the length of the adjacent side is 3 units. To find the angle theta, you would use the formula:
θ = arctan(5 / 3)
To evaluate this, you would take the arctangent of the ratio 5/3 using either a scientific calculator or a trigonometric table. The result would be the measure of the unknown angle in degrees. Make sure your calculator is set to degree mode if using a scientific calculator.
Remember, when using trigonometric functions, it's essential to consider the appropriate ratio (opposite, adjacent, or hypotenuse) based on the given information to determine which trigonometric function to use.