Question

You have a 20-foot ladder that you are using as you paint your house. You place the ladder so that it forms an angle of 30 at the point of contact between the ladder and the ground. How high will the top of the ladder be above the ground

Answer 1

First draw out the picture it will help.  Then you can see that you want the opposite segment of the angle, which leads you to use a sine.  So you have 20sin30 or 20(1/2) or 10ft.

Answer 2

Answer:

The Ladder is 10 ft high.

Step-by-step explanation

According to the question we have a 20 ft ladder inclined against a wall at a 30° angle, and are asked to find how high the top of the ladder is from the ground. I have added a visual representation to help you better understand the situation. As you can see we need to solve for x. Since we are given one angle and the hypotenuse we can solve for x using the SIN operator.

$sin(a) = \frac{opposite}{hypotenuse}$

Since we have the angle (a) and the hypotenuse we can just plug the information into the sin equation and solve for the opposite (x).

$sin(30) = \frac{x}{20ft}$

$sin(30)*20ft = x$

$0.5*20ft = x$

$10ft = x$

So now we can see that the height of the top of the ladder to the ground is 10 ft

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