Question

If tan A = 4/3 then find sin A and cosec A

Answer 1

Step-by-step explanation:

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Answer 2

Given: tan A = 4/3

To find: sin A and cosec A

Solution: In a right angled triangle ABC, there are three sides: perpendicular, base and hypotenuse.

Hypotenuse is the longest side of a right angled triangle. Any third side can be found if the length of the other two sides are known using Pythagoras' theorem.

Now, in triangle ABC:

tan A = perpendicular/base

But, tan A = 4/3 as given in the question.

Therefore, perpendicular/base = 4/3

Let perpendicular(p)=4x and base(b)=3x

Hypotenuse(h) is given by the formula:

${h}^{2} = {p}^{2} + {b}^{2}$

$= > {h}^{2} = {(4x)}^{2} + {(3x)}^{2}$

$= > {h}^{2} = 16 {x}^{2} + 9{x}^{2}$

$= > {h}^{2} = 25 {x}^{2}$

$= > h = \sqrt{25 {x}^{2} }$

=> h = 5x

In a triangle, sin A

= perpendicular/hypotenuse

= p/h

= 4x/5x

= 4/5

cosec A is reciprocal of sin A.

Therefore, cosec A

= 1/sin A

= 1/(4/5)

= 5/4

Therefore, sin A = 4/5 and cosec A = 5/4.