Here, we use the sine rule.
The sine rule states that the ratio of the sides to the sine of the angles facing that side is a constant. So, in ang given triangle with angles A, B and C and sides a, b and c respectively,
a/sinA = b/sinB = c/sinC
Using the sine rule in ΔNOP, with ∠N opposite to side n and ∠O opposite to side o.
So, o/sin∠O = n/sin∠N
Making ∠O subject of the formula, we have
∠O = sin⁻¹(osin∠N/n)
Since o = 4.6 inches, n = 5.2 inches and ∠N = 21°, substituting the values of the variable into the equation, we have
∠O = sin⁻¹(osin∠N/n)
∠O = sin⁻¹(4.6 × sin21°/5.2)
∠O = sin⁻¹(4.6 × 0.3584/5.2)
∠O = sin⁻¹(1.6485/5.2)
∠O = sin⁻¹(0.3170)
∠O = 18.5°
The other values of ∠O are the values in the second quadrant as sin∠O is positive in the first and second quadrant.
So, in the second quadrant ∠O = 180° - 18.5° = 161.5°
So, all possible values of ∠O, to the nearest 10th of a degree are 18.5° and 161.5°
Learn more about the sine rule here:
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