Respuesta :
Question:
Given tan B =7/24, find the sin B
Answer:
Option A
[tex]sin\ B = \frac{7}{25}[/tex]
Solution:
Given that,
[tex]tan\ B = \frac{7}{24}[/tex]
We have to find sin B
We know that by trignometric ratios,
[tex]tan = \frac{opposite}{adjacent}[/tex]
From given,
[tex]tan\ B = \frac{7}{24}[/tex]
On comparing we get,
Opposite = 7
Adjacent = 24
We can find the hypotenuse
[tex]hypotenuse^2 = opposite^2 + adjacent^2\\\\hypotenuse^2 = 7^2 + 24^2\\\\hypotenuse^2 = 49 + 576\\\\hypotenuse^2 = 625\\\\Take\ square\ root\ on\ both\ sides\\\\hypotenuse = 25[/tex]
Thus Sin B is given as:
[tex]sin\ B = \frac{opposite}{hypotenuse}\\\\sin\ B = \frac{7}{25}[/tex]
Thus, sin B is [tex]\frac{7}{25}[/tex]
