n ΔMNO with sides 570cm, 350cm, and 230cm, ∠O is approximately 34.96°. This was calculated using the Law of Cosines.
Solving for ∠O in ΔMNO
Given:
ΔMNO with side lengths:
m = 570 cm
n = 350 cm
o = 230 cm
To find:
Measure of ∠O (rounded to the nearest 10th of a degree)
Using the Law of Cosines:
The Law of Cosines states that for any triangle ΔABC with sides a, b, and c, and angle C opposite side c:
c² = a² + b² - 2ab * cos(C)
In our case, we want to find ∠O (opposite side o), so we can rewrite the formula as:
o² = m² + n² - 2mn * cos(∠O)
Substituting known values:
230² = 570² + 350² - 2(570)(350) * cos(∠O)
Solving for cos(∠O):
cos(∠O) = (570² + 350² - 230²) / (2 * 570 * 350)
cos(∠O) ≈ 0.8276
Finding ∠O:
∠O ≈ cos⁻¹(0.8276)
∠O ≈ 34.96° (rounded to the nearest 10th of a degree)
Therefore, the measure of ∠O in ΔMNO is approximately 34.96 degrees.