Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
The value of Tan(A - B) is -0.1295.
Trigonometry
Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
Right angle triangle
It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.
Given
Sin A = 5 ÷ 13 and Tan B = -√3.
To find
The value of tan(A - B).
How to find the value of tan(A - B)?
The angle A will be,
[tex]\begin{aligned} \rm sin A &= \dfrac{5}{13}\\\\\rm A &= \rm sin^{-1} \dfrac{5}{13}\\\\\rm A &= 22.62^o\\\\\end{aligned}\\But\ for\ the\ \dfrac{\pi}{2} < A < \pi\\\\A = 22.62^o + 90^o\\\\A = 112.62^o[/tex]
Similarly for angle B,
[tex]\begin{aligned} \rm tan B &= -\sqrt{3} \\\\\rm B &= \rm tan^{-1} -\sqrt{3} \\\\\rm B &= -60^o\\\\\end{aligned}\\\rm But\ for\ the\ \dfrac{\pi}{2} < B < \pi\\\\B = -60^o + 180^o\\\\B = 120^o[/tex]
Then tan (A - B) will be
Tan(A - B) = tan(112.62 - 120)
Tan(A - B) = tan(-7.38)
Tan(A - B) = -0.1295
Thus, the value of Tan(A - B) is -0.1295.
More about the trigonometry link is given below.
https://brainly.com/question/13710437
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.
