/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 23 At a point 50 feet from the base... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 23

At a point 50 feet from the base of a church, the angles of elevation to the bottom of the steeple and the top of the steeple are \(35^{\circ}\) and \(47^{\circ} 40^{\prime},\) respectively. Find the height of the steeple.

Short Answer

Expert verified
The height of the steeple can be found by calculating the total height (\(y\)) and the height of the church without the steeple (\(x\)) using trigonometry, and then subtracting (\(x\)) from (\(y\)).

Step by step solution

01

Set up the equations

Let鈥檚 denote \(x\) = the height of the church building without the steeple; and \(y\) = the total height of the church including the steeple. The tangent of the angles are therefore: \(tan(35^{\circ}) = \frac{x}{50}\) and \(tan(47^{\circ} 40^{\prime}) = \frac{y}{50}\)
02

Calculate the height of the building

Based on the first equation, we can calculate \(x= 50 \times tan(35^{\circ})\)
03

Calculate the total height of the church

Similarly, from the second equation, we calculate \(y = 50 \times tan(47^{\circ} 40^{\prime})\)
04

Calculate the height of the steeple

The height of the steeple can be determined by subtracting \(x\) from \(y\): Steeple height = \(y - x\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Prove each identity. (a) \(\arcsin (-x)=-\arcsin x\) (b) \(\arctan (-x)=-\arctan x\) (c) \(\arctan x+\arctan \frac{1}{x}=\frac{\pi}{2}, \quad x>0\) (d) \(\arcsin x+\arccos x=\frac{\pi}{2}\) (e) \(\arcsin x=\arctan \frac{x}{\sqrt{1-x^{2}}}\)

Sketch a graph of the function. $$f(x)=\arctan 2 x$$

A buoy oscillates in simple harmonic motion as waves go past. The buoy moves a total of 3.5 feet from its low point to its high point (see figure), and it returns to its high point every 10 seconds. Write an equation that describes the motion of the buoy where the high point corresponds to the time \(t=0\) (figure cannot copy)

Is a degree or a radian the greater unit of measure? Explain.

Graph the functions \(f\) and \(g .\) Use the graphs to make a conjecture about the relationship between the functions. $$f(x)=\sin x+\cos \left(x+\frac{\pi}{2}\right), \quad g(x)=0$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.