Answer:
Part 1) [tex]OH=9.22\ cm[/tex]
Part 2) [tex]NK=5.86\ cm[/tex]
Step-by-step explanation:
we know that
A rectangle has opposite sides parallel and congruent and the measure of the internal angles is equal to 90 degrees each
Part 1) Find the length of the zip OH
In the right triangle OLH find out the length side of the hypotenuse OH
Applying the Pythagoras Theorem
[tex]OH^2=LH^2+LO^2[/tex]
we have
[tex]LH=LM-HM[/tex]
[tex]LH=9-2=7\ cm[/tex]
[tex]LO=MN=6\ cm[/tex]
substitute the values
[tex]OH^2=7^2+6^2[/tex]
[tex]OH^2=85[/tex]
[tex]OH=\sqrt{85}\ cm[/tex]
[tex]OH=9.22\ cm\ cm[/tex]
Part 2) Find the length of the zip NK
we know that
The measure of angle LOH is equal to the measure of angle ONK, because triangle KON is a right triangle
In the right triangle LOH find the cosine of angle LOH
cos(∠LOH)=LO/OH -----> adjacent side to angle LOH divided by the hypotenuse
substitute the values
cos(∠LOH)=6/√85 -----> equation A
In the right triangle KON find the cosine of angle ONK
cos(∠ONK)=NK/ON -----> adjacent side to angle ONK divided by the hypotenuse
substitute the values
cos(∠ONK)=NK/9 -----> equation B
Remember that
cos(∠LOH)=cos(∠ONK)
equate equation A and equation B
[tex]6/\sqrt{85}=NK/9\\NK=9(6/\sqrt{85})\\NK=5.86\ cm[/tex]
Answer:
The length of the zip = 9.22cm
The length of the second zip = 5.86cm
Step-by-step explanation:
step 1:
(i) For rectangle opposite sides are equal. Therefore from the given diagram,
MN=OL=6cm.
Also ON = LM
If LH = ON - HM, then
= 9 - 2
LH = 7cm
In ΔOLH,
By pythagoras theorem,
[tex]OH^{2}[/tex]=[tex]OL^{2}[/tex]+[tex]LH^{2}[/tex]
OH =[tex]\sqrt{6^{2}+7^{2} }[/tex]
= [tex]\sqrt{36+49 }[/tex]
=[tex]\sqrt{85}[/tex]
OH = 9.22 Cm
Thus the length of the zip = 9.22 cm
step 2:
(ii) In ΔOHL
Tan(∠OHL) [tex]=\frac{opposite \ side}{adjacent\ side }[/tex]
Tan(∠OHL) [tex]=\frac{OL}{HL}[/tex]
Tan(∠OHL)[tex]=\frac{6}{7}[/tex]
Tan(∠OHL) = 0.85
∠OHL = 40.6°
In ΔKON,
Sin(∠KON) [tex]=\frac{opposite\ side}{hypotenuse\ side }[/tex]
Since opposite angles are equal,
Sin(∠OHL)[tex]=\frac{KN}{ON}[/tex]
Sin(40.6°)[tex]=\frac{KN}{9}[/tex]
0.65*9 [tex]= KN[/tex]
KN=5.86 cm
Thus, the length of the second zip [tex]=5.86\ cm[/tex]
To learn more about Pythagoras theorem, refer:
