a ladder 12 m long rests aganist a wall if it reaches the wall at a height of root 63m then find the angle of elevation
sin theta = sqrt(62)/12
To find the angle of elevation, we can use the trigonometric function called "tangent."
The angle of elevation is the angle between the ground and the ladder. In this case, the ladder is the hypotenuse of the right triangle, the height of the wall is the opposite side, and the distance from the base of the ladder to the wall is the adjacent side.
Let's label the height of the wall as "h," the distance from the base of the ladder to the wall as "d," and the angle of elevation as "θ."
Since we have the values for the height and the length of the ladder, we can use the Pythagorean theorem to find the distance from the base of the ladder to the wall:
d^2 + h^2 = 12^2
d^2 + √63^2 = 12^2
d^2 + 63 = 144
d^2 = 144 - 63
d^2 = 81
d = √81
d = 9
Now we have the values for the opposite and adjacent sides of the right triangle, so we can use the tangent function to find the angle of elevation:
tan(θ) = h / d
tan(θ) = √63 / 9
To find the angle of elevation, we need to take the inverse tangent (arctan) of both sides:
θ = arctan(√63 / 9)
Using a scientific calculator or an online calculator, we calculate the inverse tangent:
θ ≈ 25.61 degrees