toby the cat is stuck in a tree. billys dad placed a ladder 5 feet from the base of the tree and then leaned the ladder against the tree. the top of the ladder is where toby is sitting. if the ladder makes a 65 degree angle with the ground, how far up the tree is the cat?
tan 65 = h/5
The ladder and tree form a right triangle with the ground, The height
(h) is the distance from the base of the tree to the point where the ladder touches the tree.
Sin65=h/X=h/5, h=5Tan65=10.7 Feet
To determine how far up the tree Toby the cat is, we can use trigonometry. In this case, we can use the sine function since we know the angle and the distance of the ladder from the base of the tree.
First, let's label the given information:
The distance from the base of the tree to where the ladder touches the ground is 5 feet.
The angle between the ladder and the ground is 65 degrees.
Next, we can calculate the height of the tree by multiplying the distance of the ladder from the base of the tree by the sine of the angle:
Height = Distance x sin(Angle)
Plugging in the values:
Height = 5 feet x sin(65 degrees)
Now, to find the height, you can use a scientific calculator to solve for sin(65 degrees) and multiply it by 5 feet. The result will be the height at which Toby the cat is sitting in the tree.