Relation Between Altitude Base and Hypotenuse
Relation Between Altitude Base and Hypotenuse
Relation Between Altitude Base and Hypotenuse:
Let us refer to fig. again. If you want to find the height CD of the minar without actually measuring it, what information do you need? You would need to know the following:
(i) The distance DE at which the student is standing fromthe foot of the minar.
(ii) the angle of elevation, , of the top of the minar.
(iii) the height AE of the student.
Assuming that the above three conditions are known, how can we determine the height of the minar?
In the figure, CD = CB+ BD. Here, BD = AE, which is the height of the student.
To find BC, we eill use trigonometric ratios of
In , the side BC is the opposite side in relation to the known
Now, which of the trigonometric ratios can we use? Which one of them has the two values that we have and the one we need to determine? Our search narrows down to using either tan A or cot A, as these ratios involve AB and BC.
Therefore, or
, which on solving would given us BC.
By adding AE to BC, you will get the height of the minar.
Example: An electrician has to repair an electric fault on a pole of height 5 m.She needs to reach a point 1.3m below the top of the pole to undertake the repair work (see fig.) What should be the length of the ladder that she should use which, when inclined at an angle of to the horizontal, would enable her to reach the required position ? Also, how far from the foot of the pole should she place the foot of the ladder? (You may take
)
SOLUTION: In fig. the electrician is requried to reach the point B on the pole AD.
SO, BD = AD - AB = (5 - 1.3)m = 3.7 m.
Here, BC represents the ladder. We need to find its length, i.e.., the hypotenuse of the right triangle BDC.
Now, can you think which trigonometric ratio should we consider?
It should be sin .
So,
Therefore,
i.e., the length of the laddershould be 4.28 m.
Now,
i.e., (approx)
Therefore, she should place the foot of the ladder at a distance of 2.14 m from the pole.
Students / Parents Reviews [10]
Abhyas is a complete education Institute. Here extreme care is taken by teacher with the help of regular exam. Extra classes also conducted by the institute, if the student is weak.
Om Umang
10thAbout Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has always taken my doubts and suppoeted me.
Shreya Shrivastava
8thIt has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice
Barkha Arora
10thAbhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.
Manish Kumar
10thMy experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.
Ayan Ghosh
8thOne of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develope practical knowledge also.
Aman Kumar Shrivastava
10thMy experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak points.
Shivam Rana
7thBeing a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from my daughter.
Prisha Gupta
8thI have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying
Yatharthi Sharma
10thIt was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.
