4. Which equation is a correct way to calculate x?
Answer: C
tan x= 5,000/7,000
The equation tan x = 5,000/7,000 correctly represents a ratio that can be used to calculate the angle x in a right triangle where the opposite side is 5,000 and the adjacent side is 7,000.
A) sin x=5,000 /7,000
This equation is incorrect for calculating x because it implies using the sine function, which relates the opposite side to the hypotenuse, not to the adjacent side. Without knowing the hypotenuse, this equation cannot be used to find x.
B) sin x= 7,000 /5,000
Similar to option A, this equation is also incorrect since it uses the sine function, which is not applicable here. The sine function does not relate the sides in the correct manner for calculating x given the specified ratios of the opposite and adjacent sides.
C) tan x= 5,000/7,000
This equation is correct because it uses the tangent function, which is defined as the ratio of the opposite side (5,000) to the adjacent side (7,000). This is the appropriate way to calculate the angle x in a right triangle.
D) tan x=7,000/5,000
This equation is incorrect as it inverts the correct tangent ratio. It suggests that the opposite side is 7,000 and the adjacent side is 5,000, which does not align with the given values for calculating x.
Conclusion
The correct answer, tan x = 5,000/7,000, is the only option that accurately uses the tangent function to relate the sides of a right triangle, allowing for the calculation of angle x. All other options either misuse the sine function or misrepresent the ratio needed for tangent, thereby failing to provide a valid method for finding x.