Question

If cscx°=45, what is the value of b? In triangle LMN in which angle M measures 90 degrees, angle L measures x degrees, LN measures 22.5 units, and NM measures 3b units.

a) 2
b) 3
c) 4
d) 5

Answer 1

Cosecant is the hypotenuse divided by the opposite side. Given cscx°=45 and hypotenuse LN=22.5, with NM as 3b, setting up cscx°=45=22.5/(3b) and solving for b gives b=1/6, which does not match any of the provided options, suggesting an error in the question or options.

Step-by-step explanation:

If cscx°=45, we are dealing with a right-angled triangle LMN where angle M is 90 degrees and angle L is x degrees. The cosecant function (csc) is defined as the hypotenuse over the opposite side in a right triangle. Therefore, if cscx°=45, that implies the hypotenuse (LN) over the side opposite to angle L (NM) equals 45. Given that LN measures 22.5 units and NM measures 3b units:

1. cscx° = hypotenuse/opposite = LN/NM
2. 45 = 22.5/(3b)
3. Multiplying both sides of the equation by 3b gives us 135b = 22.5
4. Divide both sides by 135 to solve for b, resulting in b = 22.5 / 135 = 1/6
5. None of the options (a) 2, (b) 3, (c) 4, or (d) 5 match the result of 1/6, indicating a potential error in the question or the provided options.