perform the problem?

Question

MEASURE OF ANGLE OF ELEVATION OF THE TOP OF THE CLIFF IS 25,ON WALKING 100 METERS TOWARDS THE CLIFF,MEASURE OF ANGLE OF ELEVATION OF THE TOP IS 45 DEGREE.FIND THE HEIGHT OF THE CLIFF.

Answer 1

We do this all the time to estimate building heights. There are three simple formulae:
1. To get the missing angle: A+B+C=180°
2. To compute the Hypotenuse for the next step: Law of sines...
a/sinA=b/sinB=c/sinC for solving oblique triangles.
3. To get the adjacent side of a right triangle: Sin=O/H

So:
1. 25°+135°+A=180°...... A=20°
2. 100/sin20°=b/sin25°.... cross multiply....
100sin25°=bsin20°
b=100sin25°/sin20°
b=123.565313327... the hypotenuse for the next step
3. sin45°=h/123.565313327
h=123.565313327sin45°
h=87.373870973 meters

Answer 2

Set up the problem like this:

Let the distance from the cliff be on the x axis and the height of the cliff be on the y axis. The original distance, D, from the cliff before walking 100 meters then can be expressed by this equation:

D = 100 + h

Here h is the distance from the cliff after walking the 100 meters. We are given an important clue here. Since we know that the tangent of a 45 degree angle is equal to 1, then the height of the cliff after walking the 100 meters is also equal to h. This fact we can use in the problem later on.

Now that we know the height of the cliff is equal to h, we can use the tangent of the original angle of inclination, 25 degrees, to find out what h is.

Remembering that the equation for the tangent of an angle is:

tan A = length along y axis/length along x axis, we can set up this equation:

tangent (25 degrees) = height of cliff/original distance from base of cliff. So we get:

**tan 25 = h/(100+h)

Looking up the tangent of 25 degrees on a trig chart or on our calculator shows tan 25 is approximately 0.4663. Now we simply set equation ** above equal to this value and do the alegra.

0.4663(100+h) = h
46.63 + (0.4663)h = h
46.63 = h-(0.4663)h
46.63 = (0.5337)h
46.63/(0.5337) = h
87.37 = h

To check, we substitute our calculated value for h back into equation ** and see whether our results are correct.

.04663 = tan 25 = h/100+h = 87.37/100+87.37 = 87.37/187.37 = 0.466297.

This is close enough to the original result in almost anyone's estimation. We can conclude from this that the height of the cliff is also equal to h, or 87.37 meters.

We are done!

Answer 3

You have to solve two eqns with two variables
1) tan 45= height / awaydistance
2) tan 25 = height / (100 + away distance)

Fm #1 => height = awaydistance (because tan 45 = 1)
Fm there substitude into #2

the height of cliff = (100*tan25) / (1-tan25)

Answer 4

let the height of the cliff be h
let the distance of the initial point from the cliff be x metres
theequation is x/h=tan25
after walking 100 m towards the cliff the distance=100-x
the new equation is (100-x)/h=tan45*
=>(100-x)/h=1 as tan45*=1
so x=100-h

substituting this in thefirstequation
(100-h)/h=tan25*
100-h=htan25*
h+htan25*=100
h(1+tan25*)=100
h=100/(1+tan25*)

Answer 5

this is simple. visualise two triangles one with theta 25 and other with phi 45 and solve as u would for any trigo problem. use log tables to find the value of cos and sin of 25