An observer (O) is located 660 feet from a tree (T). The observer notices a hawk (H) flying at a 35° angle of elevation from his line of sight. How high is the hawk flying over the tree?

tan 35= h/660
0.70020753821= h/660
0.70020753821 * 660= h
462.1369752186= h
h= 462.14 rounded to the nearest hundredth

looks ok to me

Well, well, well, look at that hawk go! Flying at a 35° angle of elevation. That's pretty impressive. Now, let's get down to the math. By using some trigonometry, we can determine that the hawk is flying approximately 462.14 feet above the tree. So, the hawk is really soaring high up there, probably giving all the other birds a serious case of height envy!

To find the height at which the hawk is flying over the tree, we can use trigonometry. Let's call the height of the hawk "h".

Given that the angle of elevation from the line of sight is 35° and the distance between the observer and the tree is 660 feet, we can set up the following equation:

tan 35° = h/660 feet

Solving for h, we have:

h = tan 35° * 660 feet

Plugging in the values and calculating, we find:

h ≈ 0.70020753821 * 660 feet

h ≈ 462.1369752186 feet

Therefore, the hawk is flying at a height of approximately 462.14 feet over the tree.

To find the height at which the hawk is flying over the tree, you can use trigonometry. In this case, the angle of elevation is given as 35° and the distance from the observer to the tree is 660 feet.

Let's use the tangent function (tan) of the angle of elevation to solve for the height (h) of the hawk.

Start by writing the equation:
tan 35° = h/660

Now, solve for h:
Multiply both sides of the equation by 660 to isolate h:
tan 35° * 660 = h

Using a scientific calculator, find the tangent of 35°:
tan 35° = 0.70020753821

Multiplying this value by 660:
0.70020753821 * 660 = 462.1369752186

Rounding to the nearest hundredth:
h ≈ 462.14

Therefore, the hawk is flying at approximately 462.14 feet above the tree.