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Angle of elevation and depression word problems
The video reviews how you can use trigonometry in order to find the angle of elevation and depression.
The word problem involves calculating the angle of elevation of a wire running from a flagpole.
We are looking here at the word problems and I need to go over the angle of elevation, and what is the angle of depression? An angle of elevation works like this. If you are on the ground ,and you are looking up at the top of a tower. Your angle of elevation is the angle you form with the horizontal ground. Usually from the ground up. Sometimes you are actually going to go from your eye level and up. So an angle of elevation is this angle right here, elevating upward. From the horizontal going upward to the object. I will call this angle the angle of elevation. Now, where would the angle of depression be? It is a little deceiving. If you are at the top, and you have a horizontal reference, angle of depression is right here. It is from the horizontal at the top looking down. So always draw a horizontal and a line pointing down. Notice, these two sides are parallel, the horizontal reference lines. Really the angle of elevation and angle of depression are equal to each other because they are alternate interior angles with two parallel lines and a transversal. These two angles will be the same measure, but you will draw them in different places. Now let's get to the word problems involving elevation and depression. A 38 foot wire runs from a point on the ground to the top of a 24 foot flagpole. What is the angle of elevation of the wire?
We don't know the angle which means we need to use the inverse button. To solve we will draw a picture, label what we know, and then solve.
Let's draw the picture. We have a 38 ft wire that runs from the top of a flagpole. Lets draw a flagpole, here is the top, and a wire that runs from the ground up and the wire is 38 ft. We are told that the pole is 24 ft tall. Draw and label your picture. The pole and the ground creates a right angle so draw your right angle in. What is your angle of elevation? The angle of elevation will be from the ground up. We are looking for this angle which we will call x Which two sides do we have so we can decide on our trig function. From the angle of elevation we have opposite over hypotenuse which equals our sine function. Lets take the sign of our unknown angle x equals 24 over 38. Next, grab your calculator and use your inverse button. Take the 2nd function of sine then put in your ratio of 24/38 and the angle will be 39 degrees. So x is 39 degrees. We can stop there because the question was asking for the angle of elevation. If we needed to we could figure the top angle because ,this acute angle and the other acute angle has a sum of 90 degrees. I will call that angle y Therefore 90 - 39 = 51 degrees. If we did need to solve it.
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Tagged under: angle depression,trigonometry,trig functions,missing angles sine,cosine,tangent,Angle (Dimension),math,geometry,trig,Trigonometry (Field Of Study),maths
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