Subjects trigonometry

Angle Elevation 6C4D2A

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1. **State the problem:** Marcus is 14 feet away from a 36-foot flagpole and looks up at the top of the flagpole. We need to find the angle of elevation from Marcus to the top of the flagpole. 2. **Identify the right triangle and formula:** The situation forms a right triangle where: - The opposite side to the angle is the height of the flagpole, 36 feet. - The adjacent side is the distance from Marcus to the flagpole, 14 feet. The angle of elevation $\theta$ can be found using the tangent function: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{36}{14}$$ 3. **Calculate the tangent ratio:** $$\tan(\theta) = \frac{36}{14} = \frac{\cancel{36}}{\cancel{14}} = 2.5714$$ 4. **Find the angle $\theta$:** Use the inverse tangent (arctan) function: $$\theta = \tan^{-1}(2.5714)$$ 5. **Evaluate the angle:** Using a calculator, $$\theta \approx 68.2^\circ$$ 6. **Final answer:** The angle of elevation from Marcus to the top of the flagpole is approximately **68.2°**.