The value of sin(2x) is ![\frac{120}{169}](https://tex.z-dn.net/?f=%5Cfrac%7B120%7D%7B169%7D)
Explanation:
Given that ![tan x =\frac{12}{5}](https://tex.z-dn.net/?f=tan%20x%20%3D%5Cfrac%7B12%7D%7B5%7D)
The formula for
is ![\sin (2 x)=2 \sin x \cos x](https://tex.z-dn.net/?f=%5Csin%20%282%20x%29%3D2%20%5Csin%20x%20%5Ccos%20x)
Since, ![\tan x=\frac{o p p}{a d j}](https://tex.z-dn.net/?f=%5Ctan%20x%3D%5Cfrac%7Bo%20p%20p%7D%7Ba%20d%20j%7D)
Also, it is given that ![tan x =\frac{12}{5}](https://tex.z-dn.net/?f=tan%20x%20%3D%5Cfrac%7B12%7D%7B5%7D)
Thus,
and ![adj=5](https://tex.z-dn.net/?f=adj%3D5)
To find the hypotenuse, let us use the pythagoras theorem,
![\begin{aligned}h y p &=\sqrt{12^{2}+5^{2}} \\&=\sqrt{144+25} \\&=\sqrt{169} \\&=13\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dh%20y%20p%20%26%3D%5Csqrt%7B12%5E%7B2%7D%2B5%5E%7B2%7D%7D%20%5C%5C%26%3D%5Csqrt%7B144%2B25%7D%20%5C%5C%26%3D%5Csqrt%7B169%7D%20%5C%5C%26%3D13%5Cend%7Baligned%7D)
Now, we can find the value of sin x and cos x.
![\sin x=\frac{\text { opp }}{h y p}=\frac{12}{13}](https://tex.z-dn.net/?f=%5Csin%20x%3D%5Cfrac%7B%5Ctext%20%7B%20opp%20%7D%7D%7Bh%20y%20p%7D%3D%5Cfrac%7B12%7D%7B13%7D)
![\cos x=\frac{a d j}{h y p}=\frac{5}{13}](https://tex.z-dn.net/?f=%5Ccos%20x%3D%5Cfrac%7Ba%20d%20j%7D%7Bh%20y%20p%7D%3D%5Cfrac%7B5%7D%7B13%7D)
Now, substituting these values in the formula for sin 2x, we get,
![\begin{aligned}\sin (2 x) &=2 \sin x \cos x \\&=2\left(\frac{12}{13}\right)\left(\frac{5}{13}\right) \\&=\frac{120}{169}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Csin%20%282%20x%29%20%26%3D2%20%5Csin%20x%20%5Ccos%20x%20%5C%5C%26%3D2%5Cleft%28%5Cfrac%7B12%7D%7B13%7D%5Cright%29%5Cleft%28%5Cfrac%7B5%7D%7B13%7D%5Cright%29%20%5C%5C%26%3D%5Cfrac%7B120%7D%7B169%7D%5Cend%7Baligned%7D)
Thus, the value of sin(2x) is ![\frac{120}{169}](https://tex.z-dn.net/?f=%5Cfrac%7B120%7D%7B169%7D)
The first one is the answe
Answer:
15-3=12 to the power of 2
12 x 12 = 24
yo i suck at algebra so... you have my sincerest apolagies if this is wrong.
Step-by-step explanation:
Step-by-step explanation:
if area is = 10mm *18mm = 180mm2