We are given that $GH$ and $GJ$ are tangents to the circle from point $G$. We have $GH = 5x+3$ and $GJ = 8x-15$. We need to find the measure of $GH$.

1. Problem Description

We are given that $GH$ and $GJ$ are tangents to the circle from point $G$. We have $GH = 5x+3$ and $GJ = 8x-15$. We need to find the measure of $GH$.

2. Solution Steps

Since $GH$ and $GJ$ are tangent to the circle from the same external point $G$, their lengths must be equal. Therefore, we have

$GH = GJ$

$5x+3 = 8x-15$

Now, we need to solve for $x$.

Subtract $5x$ from both sides:

$3 = 3x - 15$

Add 15 to both sides:

$18 = 3x$

Divide both sides by 3:

$x = 6$

Now we can find the length of $GH$ by substituting $x=6$ into the expression for $GH$:

$GH = 5x+3 = 5(6)+3 = 30+3 = 33$

3. Final Answer

The measure of $GH$ is 33 feet.