If you happen to be viewing the article About Value of Tan 15? on the website Math Hello Kitty, there are a couple of convenient ways for you to navigate through the content. You have the option to simply scroll down and leisurely read each section at your own pace. Alternatively, if you’re in a rush or looking for specific information, you can swiftly click on the table of contents provided. This will instantly direct you to the exact section that contains the information you need most urgently.
This article will explain how to calculate 15 degrees of tan using trigonometry formulas. However, let us first get acquainted with the concepts of trigonometry. An angle or length in a right triangle is trigonometry. In trigonometry, lengths and angles are related to each other. The study of trigonometry involves studying the right triangle and is derived from three Greek letters, “trigono” means three and “gon” means sides, and meter means to measure.
A trigonometric ratio consists of Sine, Cosine, and Tangent. This trigonometric ratio is taken into account when designing trigonometric functions, identities, and formulas. We will use one of these trigonometric formulas to find the tangent value of 15 degrees. In addition to finding tan 15, we will also use the sine and cosine ratios as well as a trigonometry table to find the value of tan 15.
Knowing sin (15°) and cos (15°) will tell us how to find Tan (15°). When a right angle triangle is constructed, the tangent equals the ratio between the sine and cosine functions of the same angle. Thus, once we find the values for sin 15° and cos 15°, we can easily determine the tangent value. The next step in this article is to find tan 15’s value.
The value of tan (15°) is 0.26794919243. A right-angled triangle has angles that are determined by angles of a right-angled triangle, and sides that are determined by sides of the right-angled triangle. Thus, trigonometry can be defined as the measurement of triangles (specifically right-angled triangles). If one of the interior angles of a triangle is 90 degrees, the triangle is right-angled. Therefore, the three sides of the triangle can be written as follows:
-
Hypotenuse: The side opposite to the 90-degree mark on a triangle.
-
Perpendicular (opposite): It is perpendicular to the base and opposite to the unknown angle (that is, the angle between the perpendicular and the base is 90 degrees).
-
Based (adjacent): It contains both the 90 degree and unknown angle angles as well as the triangle.
Finding the Tangent
We will use the right-angled triangle shown below as an example. There are two unknown angles of less than 90 degrees (A and B). In the example above, angle A is the unknown angle, so the side measuring 5 is the hypotenuse, the side measuring 3 is the base, and the side measuring 4 is the perpendicular. If we consider angle B as , then Base and Perpendicular will be reversed.
So according to the formula of tan that is,
\[tan\Theta = \frac{Opposite}{Adjacent}\]
We can say that the tangent of angle B is the ratio of side measuring 3 over the side measuring 4 or (3/4=0.75) and the tangent of angle A is the ratio of side measuring 4 over the side measuring 3 or (4/3=1.33).
A right-angled triangle has an unknown angle of 90 degrees, so we can find the value of tan 15 if that angle is also unknown. Tan 15° is approximately 0.269 degrees.
Finding Tan 15 Value Without Using Sides:
Let us take a right angle triangle having 15 degrees as one of its angles. So, if in a right-angled triangle two angles are 90 and 15 degrees respectively, then the third angle should be:
180 – (90 + 15) = 75 degrees. The length of the base is x, perpendicular is y and hypotenuse is z.
To find tan 15 degree value we can represent 15 as 45 – 30.
tan(15°) = tan(45°-30°)
According to the formula of tan(A – B):
tan(A – B) = (tanA – tanB) /(1 + tan A tan B)
⇒tan(45°-30°) = (tan 45°- tan30°)/(1+tan 45°tan30°right-angle)
= {1- (1/√3)} / {1+(1*1/√3)}
∴ tan (15°) = (√3 – 1) / (√3 + 1)
tan (15°) = 2 – √3
On simplification, we get 0.26794919243.
Therefore,
The value of tan (15°) is 0.26794919243
Thank you so much for taking the time to read the article titled About Value of Tan 15 written by Math Hello Kitty. Your support means a lot to us! We are glad that you found this article useful. If you have any feedback or thoughts, we would love to hear from you. Don’t forget to leave a comment and review on our website to help introduce it to others. Once again, we sincerely appreciate your support and thank you for being a valued reader!
Source: Math Hello Kitty
Categories: Math
