Aptitude - Height and Distance - Discussion

@All.

According to trigonometry. We take sin θ when we should find either the opposite side value or the hypotenuse side value and we know either the hypotenuse side value or the opposite side value respectively.

Sin θ = opposite side value / Hypotenuse side value.

Same way We take cos θ when we should find either the hypotenuse side value or base side value and we know either the base side value or hypotenuse side value respectively.

Cos θ = base side value/Hypotenuse side value.

To take tan θ when we should find either the opposite side value or the base side value and we know either the base side value or the opposite side value respectively.

Tan θ = Opposite side value/base side value.

@All.

Take, Sin or Cos or Tan;

Sin = opposite/hypothesis
Cos = adjacent/hypothesis
Tan = opposite/adjacent.

Given are as following;

The angle is 60 degree.

The foot of leader is 4.6 m away from the wall (CA) this means 4.6m is adjacent,
A leader is leaning on the wall (CB) this will be hypothesis while determining (adjacent opposite or hypothesis but in real sense, it's the length of the leader!
Now, we can make out that it's Cos and not tan or sin because adjacent CA is given (4.6m) while hypothesis CB is x or unknown.

So,
Cos60 = CA/CB.
CB(x) = 4.6/cos60.
x = 9.2.

Thank You.

Its very simple @Sreeja.

If we have perpendicular (AB) and say to find hypotenuse (BC) then we use sin Angle.

If we have perpendicular (AB) and say to find Base (AC) then we use tan Angle.

If we have Base (AC) and say to find Hypotenuse (BC) then we use Cos angle.

Note : AB, AC, BC are taken from the solution of this question,

In above example, we have a base (AC) and say to the fine length of ladder means find hypotenuse (BC).

So we can use Cos Angle in this situation.

Here, why we have used COS?

Because we have to find the length of the ladder and the length of ladder is the hypotenuse, perpendicular is wall nd base is foot from the ladder so as we know cos equals base upon hypotenuse. So, to get results we will use this as the data given to us fits for cos.

By using tan you'll end up getting AB which is B the height of the wall but the problem says to find for the length of the ladder then use the value of AB and AC using Pythagorean's theorem c= √(a^2+b^2).

Then BC= √(AB^2 + AC^2) then you"ll get the length of the ladder.

sin=Opposite side/hypotenuse

cos=adjacent side/hypotenuse

tan=opposite/adjacent

AC=4.6

We know adjacent side that is only we are using cos

cos{60)=A.s/Hypo=1/2

=AC/AB = 1/2 {cross multiplication)

=2(AC)=AB

2(4.6)=AB

9.2=AB

@Nikita.

How these combinations of base and perpendicular, hypotenuse and perpendicular, hypotenuse and base and so on are formed?

Just tell where is the rule that cos will be equal to Base/Perpendicular rather than Base/Hypotenuse?

In the question, it's given that the foot of the ladder is 4.6m away from the wall. And we could take the given parameter to be either BC or AC. If it is the length of the ladder, then we should use sin and otherwise tan.

Shyam and Asish,

Absolutely we can take tan.
but if we take tan we will get AB.
Then we have to take sin to find length of the ladder, i.e BC.

It 'll take more time..so only we take cos in this problem.

Also according to the position of angle. We decide which one is opposite side and which one is adjacent. So remember the formula for each Sin, Cos, and Tan and solve the problem easily.