Answer:
DL = 5.87 un.
LN = 10.98 un.
DN = 14.4 un.
Step-by-step explanation:
<u>Given:</u>
∆DLN,
LF ⊥ DN ,
DF = 4
m∠N = 23º,
m∠D = 47º
<u>Find:</u>
DL, LN, DN
Solution:
In right triangle DFL, DF = 4, m∠D = 47º, so
![LF=DF\tan \angle D\\ \\LF=4\cdot \tan 47^{\circ}\approx 4.29 \ units](https://tex.z-dn.net/?f=LF%3DDF%5Ctan%20%5Cangle%20D%5C%5C%20%5C%5CLF%3D4%5Ccdot%20%5Ctan%2047%5E%7B%5Ccirc%7D%5Capprox%204.29%20%5C%20units)
and
![DL=\dfrac{DF}{\cos \angle D}\\ \\DL=\dfrac{4}{\cos 47^{\circ}}\approx 5.87\ units](https://tex.z-dn.net/?f=DL%3D%5Cdfrac%7BDF%7D%7B%5Ccos%20%5Cangle%20D%7D%5C%5C%20%5C%5CDL%3D%5Cdfrac%7B4%7D%7B%5Ccos%2047%5E%7B%5Ccirc%7D%7D%5Capprox%205.87%5C%20units)
In right triangle LFN, LF = 4.29 units, m∠N = 23º, so
![FN=LF\cot \angle N\\ \\FN=4.29\cdot \cot 23^{\circ}\approx 10.11\ units](https://tex.z-dn.net/?f=FN%3DLF%5Ccot%20%5Cangle%20N%5C%5C%20%5C%5CFN%3D4.29%5Ccdot%20%5Ccot%2023%5E%7B%5Ccirc%7D%5Capprox%2010.11%5C%20units)
and
![LN=\dfrac{LF}{\sin \angle N}\\ \\LN=\dfrac{4.29}{\sin 23^{\circ}}\approx 10.98\ units](https://tex.z-dn.net/?f=LN%3D%5Cdfrac%7BLF%7D%7B%5Csin%20%5Cangle%20N%7D%5C%5C%20%5C%5CLN%3D%5Cdfrac%7B4.29%7D%7B%5Csin%2023%5E%7B%5Ccirc%7D%7D%5Capprox%2010.98%5C%20units)
Hence,
DN = 4.29 + 10.11 = 14.4 units
The description for the line is solid and is shaded below the line.
<u><em>Hope this helps</em></u>
Answer:
$9 tip
Step-by-step explanation:
- Round $57.21 to the nearest $10 amount which means round it up to be $60
- Next find out how much a 15% tip would be-> 60 *0.15 = $9