Given tan A =7/24, find the sin B and tan b. A. 7/25 B. 24/7 C. 24/25 D. 7/24
1 answer:
<em><u>Question:</u></em>
Given tan B =7/24, find the sin B
<em><u>Answer:</u></em>
Option A
![sin\ B = \frac{7}{25}](https://tex.z-dn.net/?f=sin%5C%20B%20%3D%20%5Cfrac%7B7%7D%7B25%7D)
<em><u>Solution:</u></em>
Given that,
![tan\ B = \frac{7}{24}](https://tex.z-dn.net/?f=tan%5C%20B%20%3D%20%5Cfrac%7B7%7D%7B24%7D)
We have to find sin B
We know that by trignometric ratios,
![tan = \frac{opposite}{adjacent}](https://tex.z-dn.net/?f=tan%20%3D%20%5Cfrac%7Bopposite%7D%7Badjacent%7D)
From given,
![tan\ B = \frac{7}{24}](https://tex.z-dn.net/?f=tan%5C%20B%20%3D%20%5Cfrac%7B7%7D%7B24%7D)
On comparing we get,
Opposite = 7
Adjacent = 24
We can find the hypotenuse
![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](https://tex.z-dn.net/?f=hypotenuse%5E2%20%3D%20opposite%5E2%20%2B%20adjacent%5E2%5C%5C%5C%5Chypotenuse%5E2%20%3D%207%5E2%20%2B%2024%5E2%5C%5C%5C%5Chypotenuse%5E2%20%3D%2049%20%2B%20576%5C%5C%5C%5Chypotenuse%5E2%20%3D%20625%5C%5C%5C%5CTake%5C%20square%5C%20root%5C%20on%5C%20both%5C%20sides%5C%5C%5C%5Chypotenuse%20%3D%2025)
Thus Sin B is given as:
![sin\ B = \frac{opposite}{hypotenuse}\\\\sin\ B = \frac{7}{25}](https://tex.z-dn.net/?f=sin%5C%20B%20%3D%20%5Cfrac%7Bopposite%7D%7Bhypotenuse%7D%5C%5C%5C%5Csin%5C%20B%20%3D%20%5Cfrac%7B7%7D%7B25%7D)
Thus, sin B is ![\frac{7}{25}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B25%7D)
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