Find the value of m when sin ⁡m=0.53788. in triangle def, ∠f is a right angle, f=5 and e=3. find the m∠e to the nearest hundredth. a) 87.36° b) 30.96° c) 36.87° d) 53.13° answer both and show or explain answer : )

M=32.54°; m∠E = 36.87°.

To find the measure of ∠M, we take the inverse sine of both sides:

sin M = 0.53788
sin⁻¹(sin M) = sin⁻¹(0.53788)
M = 32.54°

For ΔDEF, we have the side opposite ∠E and the hypotenuse of the triangle.  Opposite/hypotenuse is the ratio for sine, so our problem looks like this:

sin E = 3/5
sin E = 0.6

Take the inverse sine of both sides:
sin⁻¹(sin E) = sin⁻¹(0.6)
E = 36.87°