A 37-ft ladder leans against a building so that the angle between the ground and the ladder is 79∘.
How high does the ladder reach on the building?
To find out how high the ladder reaches on the building, we need to use trigonometry. Specifically, we can use the sine function.
The sine function relates the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse. In this case, the opposite side represents the height of the ladder on the building, and the hypotenuse is the length of the ladder.
We have the angle between the ground and the ladder, which is 79∘, and we know the length of the ladder, which is 37 ft.
Using the sine function, we can write:
sin(angle) = opposite/hypotenuse
In this case, we have:
sin(79∘) = height/37 ft
To solve for the height, we can rearrange the equation:
height = sin(79∘) * 37 ft
Now we can calculate the height using a calculator:
height = sin(79∘) * 37 ft
height ≈ 36.67 ft
So, the ladder reaches a height of approximately 36.67 ft on the building.
To find how high the ladder reaches on the building, we can use trigonometry.
In this scenario, the ladder represents the hypotenuse of a right triangle, the ground represents the adjacent side, and the height on the building represents the opposite side.
The given angle between the ground and the ladder is 79∘.
Using the trigonometric function tangent (tan), we can set up the following equation:
tan(79∘) = height on the building / length of the ladder
Now, we can substitute the known values into the equation:
tan(79∘) = height on the building / 37 ft
To solve for the height on the building, we need to isolate it. Multiply both sides of the equation by 37 ft:
37 ft * tan(79∘) = height on the building
Calculating, we have:
37 ft * tan(79∘) ≈ 37 ft * 5.946° ≈ 55.13 ft
Therefore, the ladder reaches approximately 55.13 ft high on the building.