To solve this problem, we start with the understanding that in a right triangle, the two non-right angles are complementary. This means that angle L and angle M add up to 90 degrees:
- L + M = 90°
Given that:
- sin L = 1920
Now, the sine function gives us the ratio of the length of the opposite side to the hypotenuse in a right triangle. However, the sine value of 1920 seems incorrect because the sine function can only produce values between -1 and 1 for real angles. Hence, we need to assume there might be a misunderstanding in the problem statement.
Nonetheless, for complementary angles L and M, we know that:
- cos M = sin L
So if we correct the value of sin L to a logical value (let’s say it’s actually sin L = x, where x is within [-1, 1]), we can compute:
- cos M = sin L = x
Thus, the cosine of angle M is equal to the sine of angle L, which reinforces the relationship between these two functions in right triangles. To ultimately find the cosine of angle M, we need the correct value of sin L that adheres to the sine function’s properties.