topmath.in


practical trigonometry

heights and distance
--------------------------------------------------------------------

---------------------------------------------------------------------





 

---------------------------------------------------------------------
practical trigonometry heights and distance


A person in an helicopter flying at a height of 500 m,
observes two objects lying opposite to each other
on either bank of a river. The angles of depression
of the objects are 30 degrees and 45 degrees. Find
the width of the river.
heights distance
H = helicopter
A and C the position of the objects on the
opposite banks of the river
draw HB perpendicular to the AC

from triangle AHB
tan(30 degrees)=HB/AB
1/[sqrt(3)]=500/AB
AB = 500*sqrt(3) m ---------(1)

from triangle HBC
tan(45 degrees) = HB/BC
1=500/BC
BC = 500 m --------(2)

from (1) and (2)
AC = AB + BC = [500sqrt(3)]+500
      = 500{sqrt(3) + 1} m
width of the river = 500{1+sqrt(3)}metres
  
--------------
problem 2
An iron right circular cone of diameter 8cm
and height 12 cm is melted and recast into
spherical lead shots each of radius 4mm. How
many lead shots can be made.
Cone:
R=8/2=4cm
H=12cm
lead shot(sphere)
r = 4mm =  ( 4/10 )cm= 0.4cm

n = number of lead shots
n*volume of one lead shot = volume of cone
n*[(4/3)*pi*(r^3)]=(1/3)*pi*[R^2]*H
n=[(1/3)*pi*(R^2)*H] / [(4/3)*pi*(r^3)]
n=[(R^2)*H] / [4*(r^3)]
n = [4*4*12]/[4*0.4*0.4*0.4]
n=[3]/[0.004]
n=[3*1000]/4
n=750 lead shots




other questions and problems:


*integral calculus integration formula





----------------------------------------------------------------------------------------------
trigonometric identity and ratio of  certain standard angles

*list of differentiation formula     *integral calculus integration formula
---------------------------------------------------------------------------------------
*HOME PAGE   * mathematical formulae  * Indices, surds and some identities:   * Quadratic equations  * Progression  *Analytical Geometry * Trigonometry formula
  *Laplace Transform Inverse laplace transform *Vector
---------------------------------------------

---------------------------------------------

* Complex Number  *Hyperbolic function
disclaimer:
There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work. Also some of the companies which are displaying
advertisements may install cookies on your computer and may be tracking your browsing habits.