Question

jeff needs install security cameras on the top of shopping mall. in order to find the right location for the cameras, he must first determine the height of the building. he stands so that the angle of elevation from his horizontal line of vision to the top of the building is 20°. jeff then walks 60 feet closer to the building, and the angle of elevation of his line of sight up to the top of the building increases to 61.2°. below are the steps jeff used to determine the height of the building, where h is the height of the building above jeffs horizontal line of sight. jeffs eye level is 5.75 feet above the ground. select the first step in jeffs work which requires revision. step 1: $\tan(20°) = \frac{h}{60 + x}$ step 2: $\tan(61.2°) = \frac{x}{h}$ step 3: $0.364 \approx \frac{h}{60 + x}$ step 4: $1.819 \approx \frac{x}{h}$ step 5: $1.819h \approx x$ step 6: $0.364 \approx \frac{h}{60 + 1.819h}$ step 7: $0.364(60 + 1.819h) \approx h$ step 8: $h \approx 64.638$ step 9: the building is about 70.388 ft tall.

Explanation:

Step1: Analyze Step 1

Let's define \( x \) as the horizontal distance from Jeff's second position (after walking 60 feet closer) to the building. Then the initial horizontal distance (before walking closer) is \( 60 + x \). The height of the building above eye level is \( h \). For the angle of elevation \( 20^\circ \), the tangent should be \( \tan(20^\circ)=\frac{h}{60 + x} \), which seems correct.

Step2: Analyze Step 2

For the angle of elevation \( 61.2^\circ \), the adjacent side is \( x \) and the opposite side is \( h \), so \( \tan(61.2^\circ)=\frac{h}{x} \), not \( \frac{x}{h} \). So Step 2 has an error.

Answer:

Step 2