a fire fighter's 36 foot ladder leans against a building. the top of the ladder touches the buliding 28 ft above the ground. what is the measure of the angle of the ladder forms with the ground?
sinØ = 28/36
Ø = sin^-1 (7/9)
To find the measure of the angle that the ladder forms with the ground, we can use trigonometry. In this case, we will use the tangent function.
Tangent (θ) = Opposite / Adjacent
In the given scenario:
Opposite side = height of the building = 28 ft
Adjacent side = length of the ladder = 36 ft
Let's substitute these values into the equation:
Tangent (θ) = 28 / 36
Now, solve for θ:
θ = arctan(28 / 36)
Using a calculator, we find that:
θ ≈ 39.8 degrees (rounded to one decimal place).
Therefore, the measure of the angle that the ladder forms with the ground is approximately 39.8 degrees.
To find the measure of the angle that the ladder forms with the ground, we can use trigonometry. Specifically, we can use the inverse tangent function, also known as arctan or tan^(-1).
In this case, the ladder forms a right triangle with the ground and the building. The height of the building is given as 28 ft, and the length of the ladder is given as 36 ft.
Let's label the angle that the ladder forms with the ground as θ (theta). We can use the tangent function to relate the angle θ to the measurements of the triangle:
tan(θ) = opposite/adjacent
In this case, the opposite side is the height of the building (28 ft) and the adjacent side is the length of the ladder (36 ft). We can rearrange the equation to solve for θ:
θ = tan^(-1)(opposite/adjacent)
Substituting the given values:
θ = tan^(-1)(28/36)
Now we can calculate this angle using a scientific calculator or an online trigonometry calculator. The result is approximately 37.75 degrees.
Therefore, the measure of the angle that the ladder forms with the ground is approximately 37.75 degrees.