Aptitude - Height and Distance - Discussion

Discussion :: Height and Distance - General Questions (Q.No.5)

5. 

From a point P on a level ground, the angle of elevation of the top tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is:

[A]. 149 m
[B]. 156 m
[C]. 173 m
[D]. 200 m

Answer: Option C

Explanation:

Let AB be the tower.

Then, APB = 30° and AB = 100 m.

AB = tan 30° = 1
AP 3

AP = (AB x 3) m
= 1003 m
= (100 x 1.73) m
= 173 m.


Sripoornima.V said: (Jun 19, 2013)  
Here AP needs to be find so using the AB value Tan 30 is taken and Root 3 is 1.73 so the answer will be 173m.

Sripoornima.V said: (Jun 19, 2013)  
Here AP needs to be find so using the AB value Tan 30 is taken and Root 3 is 1.73 so the answer will be 173m.

Poorvi said: (Jun 26, 2016)  
But tan30 is 1 by root 3. Then how will 100 by root 3 becomes 173?

Aswin said: (Aug 10, 2016)  
Why we are using TAN instead of using COS?

Divyanshi Shrivastava said: (Aug 30, 2016)  
@Aswin.

We using tan because using the formula of TAN we can solve the solution easily.

Deepak Kumar said: (Sep 28, 2016)  
Easy solution with clear explanation, Thank you.

Sangeethasendhil said: (Jul 12, 2017)  
If we use sin 30 then answer will be 200, so how can I identify for correctly tan 30?

Sarthak said: (Jul 18, 2017)  
P = Perpendicular, H = Hypotenuse, B = Base.

P - B - P
H - H - B
SIN - COS - TAN

Remember this above pattern to know what to use.

For example, in the given question we were given AB (Perpendicular) and angle BPA.
We are asked to find PA (Base).
So we have to find the relation in which both (i.e; perpendicular and base includes).
Since Tan includes Perpendicular and Base both thus we will use it.

Tan30 = Perpendicular/Base,
Tan30 = AB / PA,
Tan30 = 100 / x,
1/root(3) = 100 / x,
x = 100 * root(3),
x = 100 * 1.73,
x = 173m (Ans).

Ravi said: (Jul 20, 2017)  
Why can we use tan instead using sin or cos? please tell me the solution.

Sravan said: (Jul 21, 2017)  
100 √3 has given its clear but how to calculate √3 value?

Please explain it.

Mallikarjuna said: (Aug 30, 2017)  
Hi,

Why here we are not using sin, we will get an answer of 200 if use sin but you are using the formula of tan. Can you give us an explanation?

Sankar said: (Oct 10, 2017)  
I think there is a mistake in the answer. Here really we have to use sin as what we need to find out is adjacent side.

Krishi said: (Nov 11, 2017)  
@Sankar,

In sin there is perpendicular and hypotenuse.

But we have to find base we cannot use cos also because hypotenuse is not given. Remaining tan which is used.

Vaibhav Shelar said: (Jan 31, 2018)  
No, according to 30-60-90 theorem rule answer must be 100√(3).

Yashoda Suji said: (Jun 11, 2018)  
Can't we use sin here?

Sanjau said: (Jun 26, 2018)  
√ 3 value is 1.73 and 100 x 1.73=173.

Vansh Giroh said: (Feb 15, 2019)  
Here AP needs to find so using the AB value Tan 30 is taken and root 3 is 1.73. So the answer will be 173m.

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