A tree on a 30 degree slope grows straight up. What are the measures of the greatest and smallest angles the tree makes with the hill?
To find the measures of the greatest and smallest angles the tree makes with the hill, we can use basic trigonometry and consider the slope of the hill as the reference angle.
First, let's define the slope of the hill as 30 degrees. This means that the hill makes an angle of 30 degrees with the horizontal ground.
Now, consider the tree growing straight up from the slope. Since the tree is growing straight up, it is perpendicular to the ground. Therefore, the angle between the tree and the horizontal ground is 90 degrees.
To calculate the angles the tree makes with the hill, we need to find the complementary angles to the angles we just mentioned.
The greatest angle the tree makes with the hill can be found by subtracting the slope angle from 90 degrees. In this case, it would be 90 - 30 = 60 degrees.
Similarly, the smallest angle the tree makes with the hill can be found by adding the slope angle to 90 degrees. So, it would be 90 + 30 = 120 degrees.
Therefore, the measure of the greatest angle the tree makes with the hill is 60 degrees, and the measure of the smallest angle is 120 degrees.