The ratio of opposite side of the triangle hypotenuse side of triangle is equal to sine of angle.
The expression required to fine the length of GJ is,
[tex]\sin 35=\dfrac{GJ}{9}\\[/tex]
The length of the [tex]GJ[/tex] is 5.162 units.
What is right angle triangle?
A right angle triangle is the triangle in which measure of one of the angle is equal to the 90 degrees.
The ratio of opposite side of the triangle hypotenuse side of triangle is equal to sine of angle.
Given information-
In the given triangle shown in the figure,
[tex]\angle JGH=35[/tex]
The angle [tex]\angle HJG[/tex] is right angle, which is equal to the 90 degrees.
As the sum of all the angles of a triangle is equal to the 180 degrees. Thus,
[tex]\angle JGH+\angle HJG+\angle GHJ=180\\[/tex]
Put the values,
[tex]35+90+\angle GHJ=180\\125+\angle GHJ=180\\\angle GHJ=180-125\\\angle GHJ=55[/tex]
In the given triangle, the side [tex]GJ[/tex] is the opposite side of the triangle and [tex]GH[/tex] is the hypotenuse side of the triangle.
Thus the length of the [tex]GJ[/tex] for the right triangle can be given as,
[tex]\sin 35=\dfrac{GJ}{9}\\[/tex]
This is the required expression,
[tex]GJ=\sin 35\times9\\GJ=0.574\times9\\GJ=5.162[/tex]
Thus the length of the [tex]GJ[/tex]5.162 units.
The expression required to fine the length of GJ is,
[tex]\sin 35=\dfrac{GJ}{9}\\[/tex]
The length of the [tex]GJ[/tex]5.162 units.
Learn more about the sides of a right triangle here;
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