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°**.
Angle Elevation 6C4D2A
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