Finding distance through angles and depression and hieght

Question

From a hot air balloon 4 km high, a person looks east and sees one town with angle of depression of 16°. He then looks west to see another town with angle of depression of 84°.

Answer 1

You would solve this by forming a triangle.  The angles of the triangle would be 90, 16, and 74.  The 4 km would be opposite the angle of depression.  From there, you can use the sines law to solve for the distance.

SinA/A=SinB/B.

 

Sin 16/4 = Sin 74/x  

From there, you just need to cross multiply.

 

For 84, your triangle would be 90, 84, and 6, and your equation would be Sin 84/4 = Sin Sin 6/x