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You are driving into St. Louis, Missouri, and in the distance you see the famous Gateway-to-the-West arch. This monument rises to a height of 192 $\mathrm{m}$ . You estimate your line of sight with the top of the arch to be $2.0^{\circ}$ above the horizontal. Approximately how far (in kilometers) are youfrom the base of the arch?

5.5 $\mathrm{km}$

Physics 101 Mechanics

Chapter 1

Introduction and Mathematical Concepts

Physics Basics

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Hope College

Lectures

04:16

In mathematics, a proof is…

09:56

In mathematics, algebra is…

03:40

Gateway Arch A plane is fl…

03:26

01:21

The Gateway Arch in St. Lo…

00:53

Use the following informat…

01:32

01:19

01:57

MONUMENTS At 351 feet tall…

03:10

While traveling across fla…

01:37

How Far Can You See? Becau…

Suppose you walk $18.0 \ma…

A 400 -foot tall monument …

00:31

You are driving 65 mi/h an…

03:44

04:01

A radio station located 12…

00:37

Due to the curvature of th…

02:04

PROBLEM SOLVING You are ly…

00:16

Use the formula in Exercis…

02:31

01:50

Gateway Arch The Gateway A…

01:06

The shape of the Gateway A…

All right, You're on car trips. Museum monument That right? It's 122 meters off the ground. You are very far away from it. So it appears. All right, here's your landing site. Hears you. It appears two to be about two degrees above the horizontal. All right, so we're gonna use some, uh, tricky to find the distance X right here. That this since you are from this monument. So we have the adjacent side of this triangle and we have the opposite side. We're missing the high partner, so we won't use Ah. Where's the apartment? Straight. Here's the occasion. Side here's the opposite side. During used the opposite in the adjacent sides to solve this equation. So if we use a tangent, engines off two degrees is equal opposite over adjacent. No, wait. I need you. Here is so for X so we can multiply both sides by x two x 10 Move. Two degrees is equally at 192 meters and divide both sides by tangent of two degrees and you get X is equal to 192 meters over tangent of two degrees. And if you put that into your calculator, you'll get that X is you could do 5000 498 meters. And if we convert that two kilometers, you will get that it is abolished 5.5 kilometers because there are 1000 kilometers. And when Oh, excuse me. 1000 meters and one kilometers, we divide. Um, this number right here by 1000. So we get the decimal place moves over three spots. So 12 and three right there. So 5.5 kilometers.

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