The east distance from town to house is 6.464 miles.
STEP - BY - STEP EXPLANATION
What to find? The east distance from town to house.
To solve;
Let us first make a sketch to get the clearer picture of the problem.
Attach below is the sketch.
Observe that the house is far east of the center of the town= 3miles + x
We need to find the value of x.
Using Pythagoras theorem;
hypotenuse²= adjacent² + opposite²
From the diagram above,
hypotenuse = 4
adjacent=x
opposite=2
Substitute the values into the formula and solve for x.
4² =x² + 2²
16 = x²+4
Subtract 4 from both-side of the equation.
x²=16 - 4
x²=12
Take the square root of both-side of the equation.
x = 3.464
But recall that, the east distance from town to house = 3+ x
Substitute the value of x.
Hence, the east distance from town to house = 3+ 3.464 = 6.464 miles