Geometry Homework

Question

A 20ft ladder is leaning against a 15ft wall. What is the angle of elevation?

Answer 1

Hi, Leah,

As in all geometry and trigonometry problems, draw the diagram. The ladder is on a slant, so it's the hypotenuse of the right triangle. The building is vertical (we assume), so it's the long leg of the triangle. The question about angle of elevation is asking how steep is the incline of the ladder with respect to the ground? So, look for the angle created by the flat ground (distance unknown) and the ladder. That angle is theta. From that perspective, we know the length of the opposite side (15 ft) and the hypotenuse (20 ft). Which trig function involves the opposite side and the hypotenuse? That would be Sine, right? Sine=O/H. Therefore,

Sin (theta)=15/20, which we could convert to 0.75.

You will recall that determining an angle measure when given the sides, requires the use of the inverse trig function sin^-1. Using your calculator, enter sin^-1 (0.75). You should get the answer 48.59...^o

Answer 2

If you draw a right triangle made by the ladder leaning against the wall, you can see the ladder creates a hypotenuse of 20 ft and the wall is the 15 ft side of the right triangle opposite the angle of elevation x

We can use the sin function so

sin x = 15/20

Remember to use the inverse sin function on your calculator to calculate the final value of x, and, as always, follow your basic PEMDAS order of operations

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Thanks!

Answer 3

|x

|. x

|. x <——— ladder

|. x

|. x

wall ——x———————— ground

height of wall w = 15ft

height of ladder l = 20 ft

Assuming the ladder is touching the top of the wall, the angle of elevation a is the angle between the ground and the ladder (angle between the horizontal and the line from the object (top of ladder) to the observer's eye (the line of sight).

Since there is a right angle between the wall and the ground, we can use trigonometric properties. We don’t have the distance between the wall and the bottom of the ladder so we use opposite side and hypotenuse: sin a = w / l = 15/20 = 0.75 therefore a = arcsin(0.75) = approx. 48.59