Please answer in full ASAP, pre calc word problems

Question

1.)
a flagpole casts a 24 foot long shadown when the sun is at an angle of elevation of 65 degrees. how tall is the pole?
2.)
a painter needs to reach high up the side of a house to finish a painting job. At what angle with the ground should the painter place a 20 foot ladder so that the top of the ladder reaches exactly 18 feet up the side of the house? Round your answer to the nearest tenth.
3.)
a boat leaves point A traveling at 20 mph. At the same time, another boat leaves point A traveling at 14 mph in a heading that is 80 degrees from the first boat. After 2 hours, how far apart are the two boats?

Answer 1

1)  Make a sketch as described...acute angle up from the horizontal ground to the Sun is 65^o. Said angle faces a vertical side, length h, the height of the flagpole. The shadow is the horizontal leg of the triangle. Do you remember your Geometry class?

 

tan 65 = h/24.  Put your calculator into degree mode, find the tangent of 65 degrees, and then your equation can be tweaked to solve for h.

 

2) Similar advice...make a diagram...

 

3) Let's make a sketch (diagram) for this, too.  This time, the angle A will just be 80^o.  How long will the side be for the first boat which goes 20 mph for 2 hours?  How long will other side be?  After appropriate thought, you have the situation called SAS (two sides & included angle). Use the Law of Cosines to calculate the third side.