Question

In ΔLMN, the measure of ∠N=90°, NM = 28, LN = 45, and ML = 53. What is the value of the sine of ∠M to the nearest hundredth?

Answer 1

We can use the Pythagorean theorem to find the length of LM:

LM^2 = LN^2 + NM^2
LM^2 = 45^2 + 28^2
LM^2 = 2025 + 784
LM^2 = 2809
LM = sqrt(2809)
LM = 53

Now we can use the sine function:

sin(M) = LM/LN
sin(M) = 53/45
sin(M) = 1.18 (rounded to two decimal places)

However, this value is greater than 1, which is not possible for a sine value. Therefore, there must be an error in the given measurements.