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Answer :
Final answer:
In triangle MNO, we can use the Law of Cosines to find the measure of angle O. Using the given side lengths, we can calculate the value of cos(O) and then find angle O using the inverse cosine function. The measure of angle O is approximately 100.1 degrees (rounded to the nearest tenth).
Explanation:
In triangle MNO, the measure of angle O can be found using the Law of Cosines. The law states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the two sides multiplied by the cosine of the included angle.
Using this equation, we can solve for angle O:
o^2 = m^2 + n^2 - 2mn * cos(O)
Plugging in the given values: 59^2 = 55^2 + 48^2 - 2(55)(48) * cos(O)
Simplifying and solving for cos(O):
3591 = 4065 - 5280 * cos(O)
Therefore, cos(O) = -0.1585
Using the inverse cosine function, we can find the measure of angle O:
O ≈ cos^(-1) (-0.1585) ≈ 100.1 degrees (rounded to the nearest tenth).
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