WPP #12: Unit O Concept 10-Sovling Angles of Elevation and Depression Word Problems

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     A) Robin went on a trip to New York to visit his friend that he hasn't seen for a while. As days past, he's invited to a rooftop party in central part of New York. Before he enters the building he looks up at the top of the building. From ground level, he measures the angle of elevation to the top of the building to be 72 degrees. If Robin is 25 feet away from it, what is the height of the building?

     B) Robin is now at the party and having a good time until he looks at the taller building right across the street from the one he's on and sees his friend waving at him. He measures the angle of elevation to the building his friend is on to be 32 degrees and see the angle of depression to be 44 degrees. If the buildings are 60 feet apart, how tall is the building that his friend is on?

For part A we have one side already given to us and it's 25 feet along with one degree. We'll use tangent to help us find "x" and when we put it the way I have we have: tan 72= x/25. Well we multiply 25 to both side so 25 can cancel itself out on the right and we end up with: 25 X tan 72. We plug it in to our calculator and the height of the building will be 76.9 ft.   

Here we have both buildings to show the comparison and to find the height of the taller building, which is the one his friend is on, we need to do two parts to solve the entire height of the building. You can see where I marked to be all of "x" and you'll also see "A" for the side of the triangle with the angle of 32 degrees, the same for the second triangle with the 44 degree angle. 

For part B, we have two triangles like I stated in the picture above, the first triangle will use the 32 degree angle and use tangent to solve it. We multiply 60 to both sides and we have x = 60 X tan 32. We multiply 60 to tan 32 when we plug it in to the calculator and that missing side will be 37.5 ft. We do the same work for the second triangle but we use 44 degrees this time and for that missing side we get 57.9 ft. We add 37.5 ft to 57.9 ft and we get 95.4 ft to be the height of building Robin's friend is on.