Question

after a windstorm, a leaning pole makes a 75° angle with the road surface. the pole casts a 15 - foot shadow when the sun is at a 45° angle of elevation. about how long is the pole? 11.0 ft 12.2 ft 16.7 ft 20.5 ft

Explanation:

Step1: Find the third angle of the triangle

The sum of angles in a triangle is \(180^{\circ}\). Given two angles \(75^{\circ}\) and \(45^{\circ}\), the third angle \(A=180-(75 + 45)=60^{\circ}\)

Step2: Apply the Law of Sines

The Law of Sines states that \(\frac{a}{\sin A}=\frac{b}{\sin B}\). Let the length of the pole be \(x\) (opposite the \(45^{\circ}\) angle), and the shadow length \(b = 15\) (opposite the \(60^{\circ}\) angle). So \(\frac{x}{\sin45^{\circ}}=\frac{15}{\sin60^{\circ}}\)

Step3: Solve for \(x\)

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Answer:

B. \(12.2\) ft