what is the angle of elevation of a 15 foot ladder leaning 12 feet up a building?
To find the angle of elevation, we can use trigonometry. The angle of elevation is the angle between the ground and the line of sight from the viewer to the top of the object being observed.
In this case, the ladder forms a right triangle with the ground and the wall of the building. The length of the ladder is the hypotenuse of the triangle, and the height of the wall is the opposite side. The distance from the viewer to the base of the ladder is the adjacent side.
Using the tangent function, we can find the angle of elevation:
tan(angle) = opposite/adjacent
Plugging in the given values, we have:
tan(angle) = 12/15
To find the angle, we need to take the inverse tangent (arctan) of both sides:
angle = arctan(12/15)
Using a calculator, we can evaluate this to find the angle of elevation.
To find the angle of elevation of a ladder leaning against a building, we can use basic trigonometry. The angle of elevation is the angle formed between the ground and the line of sight from the bottom of the ladder to the top of the ladder.
In this case, we have a right-angled triangle formed by the ladder, the building, and the ground. The side opposite the angle of elevation is the height of the building (12 feet), and the hypotenuse is the length of the ladder (15 feet).
To calculate the angle of elevation, we can use the inverse trigonometric function of sine. The sine of an angle is defined as the ratio of the length of the side opposite to the hypotenuse. Mathematically, we can express this as:
sin(angle) = opposite/hypotenuse
In this case, the opposite side is 12 feet and the hypotenuse is 15 feet. Plugging these values into the equation, we can solve for the angle.
sin(angle) = 12/15
To find the angle itself, we take the inverse sine (also known as arcsine) of both sides:
angle = arcsin(12/15)
Now, let me calculate the exact value of the angle for you.