Final answer:
To find all possible values of angle M in triangle MNO, we can use the law of cosines. By substituting the given values into the equation and solving for cos(M), we find two possible values for angle M: approximately 123.7° and 236.3°.
Step-by-step explanation:
In triangle MNO, we have side MO = 50 cm, side NO = 35 cm, and angle O = 83°. We need to find all possible values of angle M.
To find angle M, we can use the law of cosines. The law of cosines states that for a triangle with sides a, b, and c and angle C opposite side c, the following equation holds: c^2 = a^2 + b^2 - 2abcos(C).
Let's substitute the given values into the equation and solve for cos(M).
50^2 = 35^2 + 50^2 - 2(35)(50)cos(M)
After solving the equation, we find that cos(M) = -0.53. Taking the inverse cosine of -0.53, we find two possible values for angle M, approximately 123.7° and 236.3°.