Answer:
303.8 miles.
Step-by-step explanation:
Using the given information, draw a figure as shown below.
90 mph for 3 hours = 270 miles
100 mph of 1 hour = 100 miles
In triangle ABC,
[tex]\angle ABC=50^{\circ}+50^{\circ}=100^{\circ}[/tex]
Using cosine formula,
[tex]AC^2=AB^2+BC^2-2(AB)(BC)\cos B[/tex]
[tex]AC^2=(270)^2+(100)^2-2(270)(100)\cos (100^{\circ})[/tex]
[tex]AC^2=72900+10000-54000\cdot\left(-0.174\right)[/tex]
[tex]AC^2=92296[/tex]
Taking square root on both sides.
[tex]AC=\sqrt{92296}[/tex]
[tex]AC\approx 303.8[/tex]
Therefore, the plane is 303.8 miles from its starting point.
