Question

If two coconut trees 15 m and 25 m high are 70 m apart, then the height of the point of intersection of the line joining the top of each tree to the foot of the opposite tree is

Answer 1

Step-by-step explanation:

perpendicular height =10m

distance between two coconut trees=70m

by using Pythagoras theorem

h=root 70²+10²

h=root4900+100

h=70.7 m

Answer 2

Given:

If two coconut trees 15 m and 25 m high are 70 m apart

To Find:

the height of the point of intersection of the line joining the top of each tree to the foot of the opposite tree is

Solution:

Let us first construct a diagram to easily visualize and solve the problem, according to the diagram

AB=15m

CD=25m

BD=70m

Now to find the height OP first we will need to find the value of OB, the value of OB and OC will be in the ratio of 3:5 because triangle ABD and CDB is similar with one side ratio as 15/25=3:5 so the will also intersect the line in the same ratio, now using Pythagoras theorem to find the value of BC,

$BC^2=BD^2+CD^2\\BC^2=4900+625\\BC=\sqrt{5525} \\BC=74.33m$

Now the value of OB will be

$OB=74.33*\frac{3}{8}\\=27.87m$

So now the triangle OPB and CDB is also similar then we can write a relation as,

$\frac{OB}{CB} =\frac{OP}{CD}\\OP=\frac{27.87*25}{74.33}\\OP=9.37m$

Hence, the height of the point of intersection of the line joining the top of each tree to the foot of the opposite tree is 9.37m.