If sin A = 3/4, calculate cos A and tan A.
We will use the basic formula of sine, cosine, and tangent functions to solve the question.
Let's draw a figure according to the given question.
Let ∆ABC be a right-angled triangle, right-angled at point B.
sin A = 3/4
⇒ BC/AC = 3/4
Let BC be 3k. Therefore, hypotenuse AC will be 4k where k is a positive integer.
Applying Pythagoras theorem on ∆ABC, we obtain:
AC2 = AB2 + BC2
AB2 = AC2 - BC2
AB2 = (4k)2 - (3k)2
AB2 = 16k2 - 9k2
AB2 = 7 k2
AB = √7 k
tan A = side opposite to ∠A / side adjacent to ∠A = BC/AB = 3k / √7 k = 3/√7
Thus, cos A= √7/4 and tan A = 3/√7
If sin A = 3/4 calculate cos A and tan A.
Maths NCERT Solutions Class 10 - Chapter 8 Exercise 8.1 Question 3:
If sin A = 3/4, the value of cos A= √7/4 and tan A = 3/√7.