two students were discussing a problem in which a distant object was seen through an angle of 2.3 degrees. One student found the distance to the object using the tangent of the angle, and the other had the same answer using the sine of the angle. Write a paragrapgh explain how this was possible
well you need at least one distance measurment i would think to even start this, but i assume it is irrelevent as they want you to compare sine and tangent. so sine is opposite over hypotenuse and tangent is opposite over adjacent. both have opposite in the fomula so use that as your basis for comparing them
When angles are very small the following approximations hold:
sin(theta) ≈ theta
tan(theta) ≈ theta
(Where theta is measured in radians), so sin and tan return very nearly the same value.
2.3 degrees is 2.3*pi/180 radians → 0.0401 radians. This is small!
sin(2.3degrees) ≈ 0.040131792533
tan(2.3degrees) ≈ 0.040164148968