To find the distance between UFP and A, we need to calculate c.
Now, remember that the sum of the 3 internal angles of a triangle is equal to 180°.
So find angle B
[tex]\beta=180°-87.4°-84.4°[/tex][tex]\beta=8.2°[/tex]
Now with the law of sines calculate c:
[tex]\frac{b}{sin\beta}=\frac{c}{\sin\gamma}[/tex][tex]\frac{68}{sin(8.2°)}=\frac{c}{\sin(84.4°)}[/tex][tex]c=\frac{68*\sin(84.4°)}{\sin(8.2°)}[/tex][tex]c=474.49\text{ km}[/tex]
So the distance from A is 474.49 km
Now use this triangle to find h
You know the hypotenuse, which is equal to c=474.49km
[tex]\sin\alpha=\frac{h}{c}[/tex][tex]h=\sin\alpha *c[/tex][tex]h=\sin(87.4°)*474.49[/tex][tex]h=474\text{ km}[/tex]
