Answer:
A'B' --> 3½ in.
D'E' --> 2½ in.
R'S' --> 4 in.
Step-by-step explanation:
Scale factor is ½,
So the lengths would be halved too
<u>Answer</u>
3
<u>Explanation</u>
Y varies directly as x
Y ∝ x Inserting constant of variation, k,
Y = kx
k = Y/x
= 18/6
= 3
The trigonometric function is given as
![\tan 75^{\circ}](https://tex.z-dn.net/?f=%5Ctan%2075%5E%7B%5Ccirc%7D)
Apply the half angle identity to find the value of tan 75 ,
![\tan (\frac{u}{2})=\frac{\sin u}{1+\cos u}](https://tex.z-dn.net/?f=%5Ctan%20%28%5Cfrac%7Bu%7D%7B2%7D%29%3D%5Cfrac%7B%5Csin%20u%7D%7B1%2B%5Ccos%20u%7D)
Here,
![\tan (\frac{150^{\circ}}{2})=\frac{\sin150^{\circ}}{1+cos150^{\circ}}](https://tex.z-dn.net/?f=%5Ctan%20%28%5Cfrac%7B150%5E%7B%5Ccirc%7D%7D%7B2%7D%29%3D%5Cfrac%7B%5Csin150%5E%7B%5Ccirc%7D%7D%7B1%2Bcos150%5E%7B%5Ccirc%7D%7D)
![\tan (75^{\circ})=\frac{\frac{1}{2}}{1-\frac{\sqrt[]{3}}{2}}=\frac{\frac{1}{2}}{\frac{2-\sqrt[]{3}}{2}}^{}](https://tex.z-dn.net/?f=%5Ctan%20%2875%5E%7B%5Ccirc%7D%29%3D%5Cfrac%7B%5Cfrac%7B1%7D%7B2%7D%7D%7B1-%5Cfrac%7B%5Csqrt%5B%5D%7B3%7D%7D%7B2%7D%7D%3D%5Cfrac%7B%5Cfrac%7B1%7D%7B2%7D%7D%7B%5Cfrac%7B2-%5Csqrt%5B%5D%7B3%7D%7D%7B2%7D%7D%5E%7B%7D)
![\tan 75^{\circ}=\frac{1}{2-\sqrt[]{3}}](https://tex.z-dn.net/?f=%5Ctan%2075%5E%7B%5Ccirc%7D%3D%5Cfrac%7B1%7D%7B2-%5Csqrt%5B%5D%7B3%7D%7D)
Now rationalize the function.
![\tan 75^{\circ}=\frac{1}{2-\sqrt[]{3}}\times\frac{2+\sqrt[]{3}}{2+\sqrt[]{3}}=\frac{2+\sqrt[]{3}}{4-3}=\frac{2+\sqrt[]{3}}{1}](https://tex.z-dn.net/?f=%5Ctan%2075%5E%7B%5Ccirc%7D%3D%5Cfrac%7B1%7D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%5Ctimes%5Cfrac%7B2%2B%5Csqrt%5B%5D%7B3%7D%7D%7B2%2B%5Csqrt%5B%5D%7B3%7D%7D%3D%5Cfrac%7B2%2B%5Csqrt%5B%5D%7B3%7D%7D%7B4-3%7D%3D%5Cfrac%7B2%2B%5Csqrt%5B%5D%7B3%7D%7D%7B1%7D)
Again simplify the trigonometric function,
![\tan 75^{\circ}=2+1.732=3.732](https://tex.z-dn.net/?f=%5Ctan%2075%5E%7B%5Ccirc%7D%3D2%2B1.732%3D3.732)
Hence the answer is 3.732.