In $\Delta \mathrm{ABC}$, right-angled at $\mathrm{B}, \mathrm{AB}=24 \mathrm{~cm}, \mathrm{BC}=7 \mathrm{~cm}$. Determine :
(i) $\sin A, \cos A$
(ii) $\sin C, \cos C$

Answer

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Precalculus

NCERT Class 10 - Math

Chapter 8

Introduction to Trigonometry

Section 1

Introduction

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Video Transcript

So in the given question we have a right triangle abc, right? And we are given that A. B. Is equal to 24 centimeters. Bc is seven centimetres. And we are told to find sign A cause A. Because see and sign C. Right? So in general what we can do is if we have a triangle say we have a triangle peak you are. And there is an angle theta in the sand group, the sign of this angry theater. So this is a right angled triangle, right? And this is the Aiport news. So this is the all close inside. Faucet side to think to and this is the are just inside, right? So when we take the value of science theater, what we do is we take the ratio of the length of the opposite side divided by a high fitness. And when you take the cause of this angle costly to what we do is we take the artist inside the length of their descent side. They were in by the length of the high partners. So this is the method that we are going to use here. So before that we need to find the length of the high Putin's. Right? Which is a C. Over here. So you can use the pythagoras theorem, which says that in a triangle, in a right angled triangle, the square of the hypotenuse the square of the length of the high pony ins oh, is equal to the son of squares. Off squares. Are the are there two saints? The other two sides of the triangle? So here we have a B and B. C. Right? So a C squared is then equal to a B squared plus B C squared. Which is equal to 24 squared plus seven squared and 24 squared plus seven squared is equal to 625. From which we can write a serious equal to the square root of 16 6, 25 which is 25. So we have found the length of the high powered news as 25. So now it is easy to calculate age of this uh Econometric criminal metric ratios. Or we can say the sign of the Andrew A. Can be taken as the office. It scientist. The angle A. Is seven and the length of the high partners is 25. So sign A. Seven by 25. Similarly, when we take cause we'll take the charges inside to A. Which is 24 and divided by the high partners 25. Now when we take sign, see the artist in the opposite side. To sign the angle C. Is the side A. B. Right, So it is 24 which is the opposite side. They were led by high partners 25. And when we take because of the sand, will see they are just inside as D. C. So we will have seven. They were led by the high partners metres, which is 25 as the answer. So this is how we find the trigonometry ratios from a given right angled triangle. I hope you understood the method. Thank you.

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