Answer:
![\dfrac{2}{5}\sqrt{3}+\dfrac{3}{10}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B5%7D%5Csqrt%7B3%7D%2B%5Cdfrac%7B3%7D%7B10%7D)
Step-by-step explanation:
<u>Trigonometric Identities</u>
![\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B](https://tex.z-dn.net/?f=%5Csin%20%28A%20%5Cpm%20B%29%3D%5Csin%20A%20%5Ccos%20B%20%5Cpm%20%5Ccos%20A%20%5Csin%20B)
<u>Trigonometric ratios</u>
![\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}](https://tex.z-dn.net/?f=%5Csf%20%5Csin%28%5Ctheta%29%3D%5Cdfrac%7BO%7D%7BH%7D%5Cquad%5Ccos%28%5Ctheta%29%3D%5Cdfrac%7BA%7D%7BH%7D%5Cquad%5Ctan%28%5Ctheta%29%3D%5Cdfrac%7BO%7D%7BA%7D)
where:
is the angle- O is the side opposite the angle
- A is the side adjacent the angle
- H is the hypotenuse (the side opposite the right angle)
Using the trig ratio formulas for cosine and sine:
<u>Angles</u>
![\sin (30^{\circ})=\dfrac{1}{2}](https://tex.z-dn.net/?f=%5Csin%20%2830%5E%7B%5Ccirc%7D%29%3D%5Cdfrac%7B1%7D%7B2%7D)
![\cos (30^{\circ})=\dfrac{\sqrt{3}}{2}](https://tex.z-dn.net/?f=%5Ccos%20%2830%5E%7B%5Ccirc%7D%29%3D%5Cdfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D)
Therefore, using the trig identities and ratios:
![\begin{aligned}\sin (\angle BAC + 30^{\circ}) & = \sin (\angle BAC) \cos (30^{\circ})+\cos (\angle BAC) \sin (30^{\circ})\\\\& = \dfrac{16}{20} \cdot \dfrac{\sqrt{3}}{2} + \dfrac{12}{20} \cdot \dfrac{1}{2}\\\\& = \dfrac{16}{40}\sqrt{3}+\dfrac{12}{40}\\\\& = \dfrac{2}{5}\sqrt{3}+\dfrac{3}{10}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Csin%20%28%5Cangle%20BAC%20%2B%2030%5E%7B%5Ccirc%7D%29%20%26%20%3D%20%5Csin%20%28%5Cangle%20BAC%29%20%5Ccos%20%2830%5E%7B%5Ccirc%7D%29%2B%5Ccos%20%28%5Cangle%20BAC%29%20%5Csin%20%2830%5E%7B%5Ccirc%7D%29%5C%5C%5C%5C%26%20%3D%20%5Cdfrac%7B16%7D%7B20%7D%20%5Ccdot%20%5Cdfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%20%2B%20%5Cdfrac%7B12%7D%7B20%7D%20%5Ccdot%20%5Cdfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%26%20%3D%20%5Cdfrac%7B16%7D%7B40%7D%5Csqrt%7B3%7D%2B%5Cdfrac%7B12%7D%7B40%7D%5C%5C%5C%5C%26%20%3D%20%5Cdfrac%7B2%7D%7B5%7D%5Csqrt%7B3%7D%2B%5Cdfrac%7B3%7D%7B10%7D%5Cend%7Baligned%7D)
Answer:
S
angle S would also be an obtuse angle measuring 118°
corresponding angle
Step-by-step explanation:
Answer:
Aa 1
Step-by-step explanation:
Answer:
{(-1,0),(-8, 9), (7,0), (1,3)}
Step-by-step explanation:
number 3 is the only one with no colliding outputs.