A ladder is 13.0m long. It leans against the wall. The base of the ladder is 3.7m from the wall. What is the angle of inclination of the ladder to the nearest tenth of a degree?
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To find the angle of inclination of the ladder, we can use trigonometry. The angle of inclination can be determined using the inverse tangent function.
Let's call the angle of inclination θ. We have the opposite side, which is the distance of the ladder from the wall (3.7m), and we have the hypotenuse, which is the length of the ladder (13.0m).
Using the tangent function: tan(θ) = opposite/adjacent
In this case, the opposite side is the distance from the wall (3.7m), and the adjacent side is the length of the ladder (13.0m).
tan(θ) = 3.7/13.0
To find the angle of inclination θ, we can take the inverse tangent (arctan) of both sides:
θ = arctan(3.7/13.0)
Using a calculator, we can find the approximate value of θ:
θ ≈ 16.7 degrees (rounded to the nearest tenth of a degree)
Therefore, the angle of inclination of the ladder to the nearest tenth of a degree is approximately 16.7 degrees.
To find the angle of inclination of the ladder, we can use trigonometry. The angle of inclination is the angle formed between the ladder and the ground.
Let's label the height of the wall that the ladder is leaning against as 'h' and the angle of inclination as 'θ.'
Using trigonometry, we can say that:
sin(θ) = opposite/hypotenuse
In this case, the opposite side is the height of the wall (h), and the hypotenuse is the length of the ladder (13.0m).
sin(θ) = h/13.0
To solve for h, we can use the Pythagorean theorem:
h^2 + 3.7^2 = 13.0^2
Simplifying the equation:
h^2 + 13.69 = 169
h^2 = 169 - 13.69
h^2 = 155.31
Taking the square root of both sides:
h ≈ 12.47
Now, we can substitute h into the equation:
sin(θ) = 12.47/13.0
θ = arcsin(12.47/13.0)
Using a calculator or a trigonometric table, we find:
θ ≈ 63.9 degrees (rounded to the nearest tenth of a degree)
Therefore, the angle of inclination of the ladder is approximately 63.9 degrees.
now wait a minute, time to learn this stuff:
In a right triangle:
sin theta = opposite / hypotenuse
cos theta = adjacent / hypotenuse
tan theta = opposite / adjacent
so here we have
hypotenuse is ladder, 13
adjacent = along ground = 3.7
so
cos theta = 3.7/13