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If sin A =3/4 , calculate cos A and tan A. - CBSE Class 10 - Mathematics

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Question

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

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`

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 8: Introduction to Trigonometry
Ex. 8.10 | Q: 3 | Page no. 181
Solution If sin A =3/4 , calculate cos A and tan A. Concept: Trigonometric Ratios.
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