A 15 ft ladder is leaning against the wall. The top of the ladder reaches 10ft up the wall. What is the angle that the ladder makes with the ground?
sinθ = 10/15
To find the angle that the ladder makes with the ground, we can use trigonometry. Specifically, we can use the inverse trigonometric function, arctan (also written as tan^(-1)).
In this scenario, the ladder forms a right triangle with the ground and the wall. The ladder acts as the hypotenuse of the triangle, while the height of the wall is the opposite side, and the distance of the ladder from the wall is the adjacent side.
Using the given information, we have:
Opposite side = height of the wall = 10 ft
Hypotenuse = length of the ladder = 15 ft
Now, we can use the tangent function to calculate the angle. The tangent of an angle is the ratio of the opposite side (height) to the adjacent side (distance from the wall).
So, the equation becomes:
tan(angle) = opposite side / adjacent side
Substituting in the known values:
tan(angle) = 10 ft / distance from the wall
Now, we can solve for the angle by taking the arctan of both sides:
angle = arctan(10 ft / distance from the wall)
To determine the angle, you just need to divide the height (10 ft) by the distance from the wall. In this case, you haven't provided the distance, so you'll need to measure the distance from the wall to get the exact angle.