Answer:
15.8 feet
Step-by-step explanation:
The base of the house is at the origin. This makes the ordered pair representing it (0, 0).
The top of the shorter tree is represented by the ordered pair (13, 9). The top of the taller tree is represented by the ordered pair (10, 14).
We will use the distance formula for each.
For the shorter tree:
[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\\\\=\sqrt{(9-0)^2+(13-0)^2}\\\\=\sqrt{9^2+13^2}\\\\=\sqrt{81+169}\\\\=\sqrt{250}\approx 15.8[/tex]
For the taller tree:
[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\\\\=\sqrt{(14-0)^2+(10-0)^2}\\\\=\sqrt{14^2+10^2}\\\\=\sqrt{196+100}\\\\=\sqrt{296}\approx 17.2[/tex]
The smaller distance is 15.8.
