My Math Forum  

Go Back   My Math Forum > High School Math Forum > Trigonometry

Trigonometry Trigonometry Math Forum


Reply
 
LinkBack Thread Tools Display Modes
April 27th, 2015, 05:00 PM   #1
Newbie
 
Joined: Feb 2015
From: canada

Posts: 10
Thanks: 0

Question solving triangles

Brit and Tara are standing 8.8 m apart on a dock when they observe a
sailboat moving parallel to the dock. When the boat is equidistant between
both girls, the angle of elevation to the top of its 8.0 m mast is 51 degrees for both observers. Describe how you would calculate the angle, to the nearest degree,between Tara and the boat as viewed from Brit’s position. Justify your reasoning with calculations.


The answer should be 47 degrees, but I can't get the answer.

Last edited by skipjack; April 28th, 2015 at 12:16 AM.
rrosa522 is offline  
 
April 27th, 2015, 05:37 PM   #2
Math Team
 
Joined: Jul 2011
From: Texas

Posts: 2,756
Thanks: 1407

horizontal distance from either observer to the base of the mast is

$\displaystyle x = \frac{8}{\tan(51^\circ)}$

the base triangle formed by the two observers and the mast bottom, parallel to the water's surface, has sides $x$, $x$, $8.8$ m

let $\theta$ be the measure of each base angle of the isosceles triangle described above.

using the cosine law ...

$\displaystyle \theta = \arccos\left[\frac{1.1\tan(51^\circ)}{2}\right] \approx 47^\circ$
skeeter is offline  
April 27th, 2015, 05:53 PM   #3
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,822
Thanks: 1048

Math Focus: Elementary mathematics and beyond
Did you make a diagram?

To calculate the distance from Tara to the sailboat, $\displaystyle x$, use the tangent ratio:

$\displaystyle \tan51^\circ=\frac8x\Rightarrow x=\frac{8}{\tan51^\circ}$

With $\displaystyle \theta$ being the angle we seek, and using the cosine ratio, we have

$\displaystyle \cos\theta=\frac{4.4}{x}\Rightarrow\theta=\cos^{-1}\left(\frac{4.4}{x}\right)\approx47^\circ$
greg1313 is offline  
Reply

  My Math Forum > High School Math Forum > Trigonometry

Tags
solving, triangles



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Triangles Archonn Algebra 20 November 5th, 2012 12:35 PM
triangles tejolson Algebra 9 October 20th, 2012 10:57 AM
30-60-90 Triangles? Recipe Algebra 9 March 13th, 2010 08:19 AM
How many triangles? MATHS Algebra 2 November 6th, 2007 06:59 AM
triangles tejolson Computer Science 1 December 31st, 1969 04:00 PM





Copyright © 2018 My Math Forum. All rights reserved.