Question

Solve the right triangle (45-45-90)

Answer 1

`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)`