Final answer:
The measure of angle O in Delta MNO can be found using the law of cosines, given the lengths of sides m, n, and o. By plugging the lengths into the law of cosines formula and solving for the cosine inverse, we obtain the measure of angle O to the nearest tenth.
Step-by-step explanation:
The student is asking about angle measures within a triangle named Delta MNO. The lengths of the sides are given as m = 55 inches, n = 48 inches, and o = 59 inches. The task is to find the measure of angle O. This can be solved using the law of cosines:
c² = a² + b² - 2ab * cos(C)
where 'a' and 'b' are the lengths of the sides opposite angles A and B, and 'c' is the side opposite angle C. Applying this law with the given side lengths, you can calculate the measure (angle O) to the nearest tenth:
o² = m² + n² - 2mn * cos(O)
cos(O) = (m² + n² - o²) / (2mn)
O = cos⁻¹[(m² + n² - o²) / (2mn)]
Plugging in the side lengths:
O = cos⁻¹[(55² + 48² - 59²) / (2 * 55 * 48)]
After computing the above expression, you get the measure of angle O. The exact method of calculation will depend on whether you're using a calculator or computing the cosine inverse by hand or through another method.