Answer
The ground coordinates of the house are $~~(1131.8, 4390.2)$
The ground coordinates of the fire are $~~(2277.5, -2596.2)$
Work Step by Step
We can find the X-coordinate of the house:
$X = \frac{(a-h)~x}{f~sec~\theta-y~sin~\theta}$
$X = \frac{(7400-150)~(0.9)}{(6)~sec~4.1^{\circ}-(3.5)~sin~4.1^{\circ}}$
$X = 1131.8$
We can find the Y-coordinate of the house:
$Y = \frac{(a-h)~y~cos~\theta}{f~sec~\theta-y~sin~\theta}$
$Y = \frac{(7400-150)~(3.5)~cos~4.1^{\circ}}{(6)~sec~4.1^{\circ}-(3.5)~sin~4.1^{\circ}}$
$Y = 4390.2$
The ground coordinates of the house are $~~(1131.8, 4390.2)$
We can find the X-coordinate of the fire:
$X = \frac{(a-h)~x}{f~sec~\theta-y~sin~\theta}$
$X = \frac{(7400-690)~(2.1)}{(6)~sec~4.1^{\circ}-(-2.4)~sin~4.1^{\circ}}$
$X = 2277.5$
We can find the Y-coordinate of the fire:
$Y = \frac{(a-h)~y~cos~\theta}{f~sec~\theta-y~sin~\theta}$
$Y = \frac{(7400-690)~(-2.4)~cos~4.1^{\circ}}{(6)~sec~4.1^{\circ}-(-2.4)~sin~4.1^{\circ}}$
$Y = -2596.2$
The ground coordinates of the fire are $~~(2277.5, -2596.2)$
