Answer:
6/7
Step-by-step explanation:
The coefficient is <u>the number right in front of the variable</u>, so in this problem, the coefficient is 6/7.
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![angle \: \: \: 8 = 91°](https://tex.z-dn.net/?f=angle%20%5C%3A%20%20%5C%3A%20%20%5C%3A%208%20%3D%2091%C2%B0)
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Answer:
![\displaystyle d \approx 15.8768](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%5Capprox%2015.8768)
Step-by-step explanation:
We want to find the distance of <em>d</em> or AB.
From the right triangle with a 35° angle, we know that:
![\displaystyle \tan 35^\circ = \frac{50}{PB}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctan%2035%5E%5Ccirc%20%20%3D%20%5Cfrac%7B50%7D%7BPB%7D)
And from the right triangle with a 42° angle, we know that:
![\displaystyle \tan 42^\circ = \frac{50}{PA}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctan%2042%5E%5Ccirc%20%20%3D%20%5Cfrac%7B50%7D%7BPA%7D)
AB is PA subtracted from PB. Thus:
![\displaystyle d = AB = PB - PA](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%3D%20AB%20%3D%20PB%20-%20PA)
From the first two equations, solve for PB and PA:
![\displaystyle \frac{1}{\tan 35^\circ } = \frac{PB}{50} \Rightarrow PB = \frac{50}{\tan 35^\circ}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B%5Ctan%2035%5E%5Ccirc%20%7D%20%20%3D%20%5Cfrac%7BPB%7D%7B50%7D%20%5CRightarrow%20PB%20%3D%20%5Cfrac%7B50%7D%7B%5Ctan%2035%5E%5Ccirc%7D)
And:
![\displaystyle \frac{1}{\tan 42^\circ } = \frac{PA}{50} \Rightarrow PA = \frac{50}{\tan 42^\circ}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B%5Ctan%2042%5E%5Ccirc%20%7D%20%3D%20%5Cfrac%7BPA%7D%7B50%7D%20%5CRightarrow%20PA%20%3D%20%5Cfrac%7B50%7D%7B%5Ctan%2042%5E%5Ccirc%7D)
Therefore:
![\displaystyle d = AB = \frac{50}{\tan 35^\circ} - \frac{50}{\tan 42^\circ}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%20%3D%20AB%20%3D%20%5Cfrac%7B50%7D%7B%5Ctan%2035%5E%5Ccirc%7D%20-%20%5Cfrac%7B50%7D%7B%5Ctan%2042%5E%5Ccirc%7D)
Using a calculator:
![\displaystyle d= AB \approx 15.8768](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%3D%20AB%20%5Capprox%2015.8768)
Answer:
The answer is y = 3/4 + 5