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Solve the right triangle (45-45-90)

Solve the right triangle (45-45-90)-example-1
User Coliff
by
8.1k points

1 Answer

11 votes

Answer:


HI=HJ=√(30)units


\angle I=45^(\circ)

Explanation:

We are given that


\angle J=45^(\circ)


JI=2√(15)units

We know that


sin\theta=(Perpendicular\;side)/(hypotenuse)

Using the formula


sin45=(HI)/(2√(15))


(1)/(√(2))* 2√(15)=HI

Where
sin45^(\circ)=(1)/(√(2))


(2√(15)* √(2))/(√(2)* √(2))=HI

By using rationalization


HI=√(30) units


Cos45=(HJ)/(2√(15))

Using the formula


cos\theta=(base)/(hypotenuse)


(1)/(√(2))* 2√(15)=HJ


(2√(15)* √(2))/(√(2)* √(2))=HJ


HJ=√(30) units

When two sides are equal then angle made by two equal sides are equal

Therefore,


\angle J=\angle I=45^(\circ)

User Paul Graffam
by
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