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Expert: Sherry Wallin - 4/10/2009


Question
HOw do you find the angle of elevation only given two of the triangles side lengths but nothing else?

Answer

elev
Hi Krishlynn Buck~
    It is unclear to me what you mean by 'only given two of the triangles side lengths'. Does this mean you have two triangles or does it mean that you have a single triangle and all you have is the length of two of the sides of this one triangle? I am going to assume the latter. So put the triangle in an x-y coordinate system. Let me explain by example. Suppose you have a triangle that has two sides measuring 5in and 6in. Place the triangle's vertex at the origin so that one of the sides is laying on either the x axis. I'm going to place this triangles vertex at the origin that the 6 in side lays on the x axis. This means the other side, the 5 in side is in first quadrant increasing left to right. This also means the angle of elevation is the angle (call it theta) at that vertex. Draw a vertical line from the end of the 5 in side down to the x axis. Let's pretend this happens at x = 4. So the point where the 5 in side and the vertical line meet is(4, y). You can find the length of the vertical by using the Pythagorean Theorem. 5^2 = y^2 + 4^2 -> 25 = y^2 + 16. Solve for y. y = 3. This is the height of the triangle. You now have enough information to calculate the angle. I assume you have had at least trigonometry so the elevation is sin (4/5)= theta or theta is about .717.

A couple of things to note: you may be thinking that you aren't using the same triangle anymore but notice the angle did not change when you dropped the perpendicular (vertical line) and that is really what you were looking for, the angle. Keep in mind that an angle of elevation is going to be an angle between 0 and 90 degrees. I have made a drawing (attached)and the red is the original two sides of the triangle.

If you have more questions or need further explanation please feel free to ask.

Math Prof

Sherry Wallin

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

Education/Credentials
I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

Awards and Honors
Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

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