Question

if sin=5/13 then the value of tan is​

Answer 1

Answer:

Tan value is 5/12

Step-by-step explanation:

Hope this helps u

Answer 2

The value of tan A is​ $\frac{5}{12}$ when sin A = $\frac{5}{13}$.

Correct question:

If sin A = $\frac{5}{13}$ then the value of tan A is​

Concept used:

Express sin A in terms of perpendicular and hypotenuse and then determine the third side of the triangle by using Pythagoras theorem.

Then find the value of tan A .

Given:

sin A = $\frac{5}{13}$

To find:

The value of tan A

Solution:

Step 1: Find base by using Pythagoras theorem in triangle ABC:

sin A = $\frac{5}{13} = \frac{perpendicular}{hypotenuse } = \frac{BC}{AC}$

From the figure, perpendicular (BC) = 5 & hypotenuse (AC) = 13

By using Pythagoras theorem in ∆ABC,

AC² = AB² + BC²

13² = AB² + 5²

169 = AB² + 25

169 - 25 = AB²

144 = AB²

AB = √144

AB = 12

Step 2 : Find the value of tan A:

tan A = $\frac{BC}{AB} = \frac{P}{B}$

tan A = $\frac{5}{12}$

Hence, the value of tan A is​ $\frac{5}{12}$ .

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