In ΔOPQ, the measure of ∠Q=90°, QO = 61 feet, and OP = 83 feet. Find the measure of ∠O .

∠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°.

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step-by-step explanation: