Question

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

Answer 1

Answer:

$GH < HJ$

Step-by-step 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, $GH < HJ$

Answer 2

Answer:

GH > HJ

The correct symbol is " >" (greater)

Step-by-step explanation:

we know that

In the triangle GHJ applying the law of sines

$\frac{GH}{sin(J)}=\frac{HJ}{sin(G)}$

substitute the given values

$\frac{GH}{sin(40\°)}=\frac{HJ}{sin(70\°)}$

Isolate GH

$GH=\frac{HJ}{sin(70\°)}(sin(40\°))$

$GH=1.46(HJ)$

therefore

GH > HJ

The correct symbol is " >" (greater)