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Sagot :
Answer:
[tex]HI=HJ=\sqrt{30}[/tex]units
[tex]\angle I=45^{\circ}[/tex]
Step-by-step explanation:
We are given that
[tex]\angle J=45^{\circ}[/tex]
[tex]JI=2\sqrt{15}[/tex]units
We know that
[tex]sin\theta=\frac{Perpendicular\;side}{hypotenuse}[/tex]
Using the formula
[tex]sin45=\frac{HI}{2\sqrt{15}}[/tex]
[tex]\frac{1}{\sqrt{2}}\times 2\sqrt{15}=HI[/tex]
Where [tex]sin45^{\circ}=\frac{1}{\sqrt{2}}[/tex]
[tex]\frac{2\sqrt{15}\times \sqrt{2}}{\sqrt{2}\times \sqrt{2}}=HI[/tex]
By using rationalization
[tex]HI=\sqrt{30}[/tex] units
[tex]Cos45=\frac{HJ}{2\sqrt{15}}[/tex]
Using the formula
[tex]cos\theta=\frac{base}{hypotenuse}[/tex]
[tex]\frac{1}{\sqrt{2}}\times 2\sqrt{15}=HJ[/tex]
[tex]\frac{2\sqrt{15}\times \sqrt{2}}{\sqrt{2}\times \sqrt{2}}=HJ[/tex]
[tex]HJ=\sqrt{30}[/tex] units
When two sides are equal then angle made by two equal sides are equal
Therefore,
[tex]\angle J=\angle I=45^{\circ}[/tex]
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