com/app/student/3694486/26545770/79af1c669f0ceba6c9bafda2fd1ababo Intro to Proof I Scho.. TypingTest.com-C... Westfield High Scho_ Do Now \( 9 / 21-9 / 22 \) From his eye, which stands 1.55 meters above the ground, Jaxon measures the angle of elevation to the top of a prominent skyscraper to be \( 67^{\circ} \). If he is standing at a horizontal distance of 266 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest tenth of a meter if necessary. \( \vdots \)

To determine the height of the skyscraper, we can use trigonometric relationships involving right triangles. Here's a step-by-step solution: ### **Given:** - **Height of Jaxon's eye above the ground:** \( 1.55 \) meters - **Horizontal distance from the base of the skyscraper:** \( 266 \) meters - **Angle of elevation to the top of the skyscraper:** \( 67^\circ \) ### **Objective:** Find the total height of the skyscraper. ### **Approach:** 1. **Visual Representation:** Imagine a right triangle where: - The **adjacent side** (base) is the horizontal distance from Jaxon to the skyscraper: \( 266 \) meters. - The **opposite side** is the difference between the skyscraper's height (\( H \)) and Jaxon's eye level (\( 1.55 \) meters). - The **angle of elevation** is \( 67^\circ \). 2. **Trigonometric Relationship:** The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side: \[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \] Plugging in the known values: \[ \tan(67^\circ) = \frac{H - 1.55}{266} \] 3. **Solving for \( H \):** Rearrange the equation to solve for \( H \): \[ H - 1.55 = 266 \times \tan(67^\circ) \] \[ H = 266 \times \tan(67^\circ) + 1.55 \] 4. **Calculating \( \tan(67^\circ) \):** Using a calculator: \[ \tan(67^\circ) \approx 2.35585 \] 5. **Plugging in the Values:** \[ H = 266 \times 2.35585 + 1.55 \] \[ H \approx 626.6551 + 1.55 \] \[ H \approx 628.2051 \text{ meters} \] 6. **Rounding the Answer:** Rounding to the nearest tenth of a meter: \[ H \approx 628.2 \text{ meters} \] ### **Answer:** The height of the skyscraper is approximately **628.2 meters**.