Respuesta :
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
