The other two vertices are (-3,6) and (-6,3)
12 1/2
Mark brainliest please
Hope this helps
Answer:
Step-by-step explanation
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Given:
![\cos 15^{\circ}](https://tex.z-dn.net/?f=%5Ccos%2015%5E%7B%5Ccirc%7D)
To find:
The exact value of cos 15°.
Solution:
![$\cos 15^{\circ}=\cos\frac{ 30^{\circ}}{2}](https://tex.z-dn.net/?f=%24%5Ccos%2015%5E%7B%5Ccirc%7D%3D%5Ccos%5Cfrac%7B%2030%5E%7B%5Ccirc%7D%7D%7B2%7D)
Using half-angle identity:
![$\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos (x)}{2}}](https://tex.z-dn.net/?f=%24%5Ccos%20%5Cleft%28%5Cfrac%7Bx%7D%7B2%7D%5Cright%29%3D%5Csqrt%7B%5Cfrac%7B1%2B%5Ccos%20%28x%29%7D%7B2%7D%7D)
![$\cos \frac{30^{\circ}}{2}=\sqrt{\frac{1+\cos \left(30^{\circ}\right)}{2}}](https://tex.z-dn.net/?f=%24%5Ccos%20%5Cfrac%7B30%5E%7B%5Ccirc%7D%7D%7B2%7D%3D%5Csqrt%7B%5Cfrac%7B1%2B%5Ccos%20%5Cleft%2830%5E%7B%5Ccirc%7D%5Cright%29%7D%7B2%7D%7D)
Using the trigonometric identity: ![\cos \left(30^{\circ}\right)=\frac{\sqrt{3}}{2}](https://tex.z-dn.net/?f=%5Ccos%20%5Cleft%2830%5E%7B%5Ccirc%7D%5Cright%29%3D%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D)
![$=\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}](https://tex.z-dn.net/?f=%24%3D%5Csqrt%7B%5Cfrac%7B1%2B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%7D%7B2%7D%7D)
Let us first solve the fraction in the numerator.
![$=\sqrt{\frac{\frac{2+\sqrt{3}}{2}}{2}}](https://tex.z-dn.net/?f=%24%3D%5Csqrt%7B%5Cfrac%7B%5Cfrac%7B2%2B%5Csqrt%7B3%7D%7D%7B2%7D%7D%7B2%7D%7D)
Using fraction rule: ![\frac{\frac{a}{b} }{c}=\frac{a}{b \cdot c}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7Ba%7D%7Bb%7D%20%7D%7Bc%7D%3D%5Cfrac%7Ba%7D%7Bb%20%5Ccdot%20c%7D)
![$=\sqrt{\frac {2+\sqrt{3}}{4}}](https://tex.z-dn.net/?f=%24%3D%5Csqrt%7B%5Cfrac%20%7B2%2B%5Csqrt%7B3%7D%7D%7B4%7D%7D)
Apply radical rule: ![\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7B%5Cfrac%7Ba%7D%7Bb%7D%7D%3D%5Cfrac%7B%5Csqrt%5Bn%5D%7Ba%7D%7D%7B%5Csqrt%5Bn%5D%7Bb%7D%7D)
![$=\frac{\sqrt{2+\sqrt{3}}}{\sqrt{4}}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B%5Csqrt%7B2%2B%5Csqrt%7B3%7D%7D%7D%7B%5Csqrt%7B4%7D%7D)
Using
:
![$=\frac{\sqrt{2+\sqrt{3}}}{2}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B%5Csqrt%7B2%2B%5Csqrt%7B3%7D%7D%7D%7B2%7D)
![$\cos 15^\circ=\frac{\sqrt{2+\sqrt{3}}}{2}](https://tex.z-dn.net/?f=%24%5Ccos%2015%5E%5Ccirc%3D%5Cfrac%7B%5Csqrt%7B2%2B%5Csqrt%7B3%7D%7D%7D%7B2%7D)
Let us draw a triangle ABC with A=15° ,B=113° and b=7.
Please see the attached image.
We know that the sum of interior angles of a triangle is 180 degrees. Thus, we have
![A+B+C=180\\ \\ 15+113+C= 180\\ \\ C=62^{\circ}](https://tex.z-dn.net/?f=A%2BB%2BC%3D180%5C%5C%0A%5C%5C%0A15%2B113%2BC%3D%20180%5C%5C%0A%5C%5C%0AC%3D62%5E%7B%5Ccirc%7D)
Apply Sine rule in the triangle ABC, we get
![\frac{a}{\sin 15}= \frac{7}{\sin 113}\\ \\ a=\frac{7 \sin 15}{\sin 113}\\ \\ a=1.97\\ \\ \text{Again apply sine rule, we get}\\ \\ \frac{c}{\sin 62}= \frac{7}{\sin 113}\\ \\ c=\frac{7 \sin 62}{\sin 113}\\ \\ c=6.71](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7B%5Csin%2015%7D%3D%20%5Cfrac%7B7%7D%7B%5Csin%20113%7D%5C%5C%0A%5C%5C%0Aa%3D%5Cfrac%7B7%20%5Csin%2015%7D%7B%5Csin%20113%7D%5C%5C%0A%5C%5C%0Aa%3D1.97%5C%5C%0A%5C%5C%0A%5Ctext%7BAgain%20apply%20sine%20rule%2C%20we%20get%7D%5C%5C%0A%5C%5C%0A%5Cfrac%7Bc%7D%7B%5Csin%2062%7D%3D%20%5Cfrac%7B7%7D%7B%5Csin%20113%7D%5C%5C%0A%5C%5C%0Ac%3D%5Cfrac%7B7%20%5Csin%2062%7D%7B%5Csin%20113%7D%5C%5C%0A%5C%5C%0Ac%3D6.71)
Therefore, we have
![a=1.97\\ c=6.71\\ C=62^{\circ}](https://tex.z-dn.net/?f=a%3D1.97%5C%5C%0Ac%3D6.71%5C%5C%0AC%3D62%5E%7B%5Ccirc%7D)