1. A 16-foot ladder on ground level is leaning against a house. If the base of the ladder is placed 5.0 feet from the house, what is the angle formed at the top of the ladder?
A. 24°
B. 18°
C. 72°
D. 20°
please help I don't know how to do this
It is always good to draw a picture. You have a right triangle with hypotenuse of 16. The side opposite the angle that you are looking for is 5.
If you take the opp/hypotenuse = sine of the angle
5/16 = sin of angle.
You can use your calculator to find the value of the angle. This is the angle whose sine is 5/16 or .3125.
If you have trouble figuring that out. you can take the sin of each of the angles given and see if that value equals .3125 which is 5/16.
20.5
To find the angle formed at the top of the ladder, you can use trigonometry. Specifically, you can use the tangent function.
Let's define a right triangle with the ladder as the hypotenuse, the distance from the base of the ladder to the house as the adjacent side, and the height of the ladder (the distance from the ground to the top of the ladder) as the opposite side.
Using the tangent function, we have:
tan(angle) = opposite/adjacent
In this case, the opposite side is the height of the ladder, which is 16 feet, and the adjacent side is the distance from the base of the ladder to the house, which is 5 feet.
tan(angle) = 16/5
To find the angle, we can take the inverse tangent (also known as arctan or tan^(-1)) of both sides:
angle = arctan(16/5)
Using a calculator, we find that arctan(16/5) is approximately 72.13 degrees.
Since the available answer choices are in degrees, we need to round this value to the nearest degree. Therefore, the angle formed at the top of the ladder is approximately 72 degrees.
The correct answer choice is C. 72°.