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If sin A =3/4 , calculate cos A and tan A. - Mathematics

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If `sin A =3/4` , calculate cos A and tan A.

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Solution

Let ΔABC be a right-angled triangle, right-angled at point B.

Given that,

sin A = 3/4

`(BC)/(AC) = 3/4`

Let BC be 3k. Therefore, AC will be 4k, where k is a positive integer.

Applying Pythagoras theorem in ΔABC, we obtain

AC2 = AB2 + BC2

(4k)2 = AB2 + (3k)2

16k 2 − 9k 2 = AB2

7k 2 = AB2

AB = sqrt7k

`cos A = ("Side adjacent to"angleA)/"Hypotenuse"`

=`(AB)/(AC) = sqrt(7k)/(4k) = sqrt7/4`

`tan A = ("Side adjacent to"angleA)/("Side adjacent to"angleA)`

`= (BC)/(AB) = (3k)/(sqrt7k) = 3/sqrt7`

Concept: Trigonometric Ratios
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APPEARS IN

NCERT Class 10 Maths
Chapter 8 Introduction to Trigonometry
Exercise 8.1 | Q 3 | Page 181
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