Answer:
∠O ≈ 43°
Step-by-step explanation:
Draw a diagram to help you visualize (see photo below).
Since ∠Q is a right angle and ΔOPQ is a triangle, we can use the trigonometric ratios (SohCahToa).
To find ∠O (which is represented by θ in the diagram), use the given sides:
QO = 61 feet
OP = 83 feet
OP is the hypotenuse since it's the longest side.
If ∠O = θ (angle of reference), then side QO is adjacent.
The trig. ratio that uses adjacent and hypotenuse is:
cosθ = adjacent / hypotenuse
Substitute the variables for this question
cosO = QO / OP
Substitute the known values
cosO = 61 feet / 83 feet Isolate "O"
∠O = cos⁻¹(61/83) Input into calculator
∠O ≈ 42.69787...° Exact answer
∠O ≈ 43° Round to the nearest whole degree
Therefore, the measure of ∠O is 43°.
Please comment below if you have any questions!
