If cos A = 4/5 , then the value of tan A is
a. 3/5
b. 3/4
c. 4/3
d. 5/3
Solution:
Given, cos A = 4/5
We have to find the value of tan A.
We know, cos x = adjacent/hypotenuse
Adjacent = 4
Hypotenuse = 5
Using the pythagorean theorem,
(hypotenuse)² = (opposite)² + (adjacent)²
(5)² = (opposite)² + (4)²
25 = (opposite)² + 16
(opposite)² = 25 - 16
(opposite)² = 9
Taking square root,
Opposite = 3
We know, tan A = opposite/adjacent
tan A = 3/4
Therefore, the value of tan A is 3/4.
✦ Try This: If sin B = 2√5/6, then the value of cos B is
Given, sin B = 2√5/6
We have to find the value of cos B.
We know that sin x = opposite/hypotenuse
Opposite = 2√5
Hypotenuse = 6
Using the pythagorean theorem,
(hypotenuse)² = (opposite)² + (adjacent)²
(6)² = (adjacent)² + (2√5)²
36 = (adjacent)² + 20
(adjacent)² = 36 - 20
(adjacent)² = 16
Taking square root,
adjacent = 4
We know that cos B = adjacent / hypotenuse
Cos B = 4/6
Therefore, the value of cos B is 4/6.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8
NCERT Exemplar Class 10 Maths Exercise 8.1 Problem 1
If cos A = 4/5 , then the value of tan A is a. 3/5, b. 3/4, c. 4/3, d. 5/3
Summary:
Tangent is the ratio of the opposite side and the adjacent side of the angle in consideration in a right-angled triangle.If cos A = 4/5 , then the value of tan A is 3/4
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