Question

Help me please asap I need to know fully how to solve this problem

Answer 1

Consider the absolute value, because we only worry about the quadrant later.


`\text{Consider: } sin(A) = |-(√(3))/(4)|`

`sin(A) = (√(3))/(4)`

Thus, we know that the hypotenuse has a length of 4 units, and the side opposite the angle, A is √3, because this is the nature of the sine function in relation to its triangular component.

The missing side can be found using Pythagoras' Theorem:
4² - (√3)² = x²
16 - 3 = x²
13 = x²
x = √13


`\therefore tan(A) = \pm \sqrt{(3)/(13)}`

Since angle A is in the third quadrant, the tangent function will produce a positive angle.


`tan(A) = \sqrt{(3)/(13)}`

`\text{Rationalise the denominator: } (√(3))/(√(13)) \cdot (√(13))/(√(13))`


`tan(A) = (√(39))/(13)`