Question

If G = 70° and J = 40°, then GH ___ HJ. Choose the correct symbol to put in the blank.

Answer 1

GH > HJ

The correct symbol is " >" (greater)

Explanation:

we know that

In the triangle GHJ applying the law of sines

`(GH)/(sin(J))=(HJ)/(sin(G))`

substitute the given values

`(GH)/(sin(40\°))=(HJ)/(sin(70\°))`

Isolate GH

`GH=(HJ)/(sin(70\°))(sin(40\°))`

`GH=1.46(HJ)`

therefore

GH > HJ

The correct symbol is " >" (greater)

Answer 2

`GH < HJ`

Explanation:

We are given that

`\angle G=70^(\circ)`

`\angle J=40^(\circ)`

We have to fill the correct symbol in the blank space.

Greater angle and greater side theorem: It states that when

`\angle A>\angle B`

Then, Opposite side to angle A > opposite side to angle B.

When Opposite side to angle A > opposite side to angle B

Then,
`\angle A >\angle B`

Side opposite to angle J=GH

Side opposite to angle G=HJ

Using the above theorem,

`\angle G >\angle J`

Then,
`HJ >GH`

Hence,
`GH < HJ`