**Problem Statement:**A spectator in the stands spots the team mascot on the field at an angle of depression of 46 degrees. If the spectator is sitting 35 feet above the ground, what is the horizontal distance between the spectator and the mascot?---**Guidance for Solution:**To solve this problem, one can use trigonometric principles, specifically the tangent function which relates angles and side lengths in right triangles.- **Tangent of an Angle**: \[ \tan(\theta) = \frac{\text{Opposite Side}}{\text{Adjacent Side}} \]In this scenario:- The angle of depression (46 degrees) relates to the angle of elevation from the mascot to the spectator.- The opposite side is the vertical height difference (35 feet).- The adjacent side is the horizontal distance we need to find.Setting up the equation:\[ \tan(46^\circ) = \frac{35}{\text{Horizontal Distance}}\]Solve for the Horizontal Distance:\[\text{Horizontal Distance} = \frac{35}{\tan(46^\circ)}\]---**Rounding Instructions:**After calculating, round the answer to the nearest tenth.**Sample Answer:**4.2

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A spectator in the stands spots the team mascot on the field at an angle of depression of 46. If the spectator is sitting 35 feet above the ground, what is the horizontal distance between the spectactor and the mascot?

A spectator in the stands spots the team mascot on the field at an angle of depression of 46. If the spectator is sitting 35 feet above the ground, what is the horizontal distance between the spectactor and the mascot?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

**Problem Statement:**

A spectator in the stands spots the team mascot on the field at an angle of depression of 46 degrees. If the spectator is sitting 35 feet above the ground, what is the horizontal distance between the spectator and the mascot?

---

**Guidance for Solution:**

To solve this problem, one can use trigonometric principles, specifically the tangent function which relates angles and side lengths in right triangles.

- **Tangent of an Angle**:
\[
\tan(\theta) = \frac{\text{Opposite Side}}{\text{Adjacent Side}}
\]

In this scenario:
- The angle of depression (46 degrees) relates to the angle of elevation from the mascot to the spectator.
- The opposite side is the vertical height difference (35 feet).
- The adjacent side is the horizontal distance we need to find.

Setting up the equation:
\[
\tan(46^\circ) = \frac{35}{\text{Horizontal Distance}}
\]

Solve for the Horizontal Distance:
\[
\text{Horizontal Distance} = \frac{35}{\tan(46^\circ)}
\]

---

**Rounding Instructions:**

After calculating, round the answer to the nearest tenth.

**Sample Answer:**
4.2

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