Question

(07.04 LC) As shown below, 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. What equation and trigonometric function can be used to solve for the height (h) of the hawk? What is the height of the hawk? You must show all work and calculations to receive full credit. (10 points) A right triangle is shown with one leg measuring 660 and another leg measuring h. One angle is marked 35 degrees.

Answer 1

The equation and trigonometric function that can be used to solve for the height (h) of the hawk is $tan \ 35^\circ = \frac{h}{660}$ OR h = 660 tan35°

The height of the hawk is 462 feet.

Trigonometry: Angles of elevation

From the question, we are to determine the height (h) of the hawk

From the diagram,

Opposite = h

Adjacent = 660 feet

Included angle = 35°

Then,

By using SOH CAH TOA, we can write that

$tan \ 35^\circ = \frac{h}{660}$

∴ h = 660 tan35°

Hence, the equation and trigonometric function that can be used to solve for the height (h) of the hawk is $tan \ 35^\circ = \frac{h}{660}$ OR h = 660 tan35°

Now, for the height of the hawk

Using the equation,

$tan \ 35^\circ = \frac{h}{660}$

h = 660 tan35°

h = 660 × 0.7002

h = 462.132 feet

h ≅ 462 feet

Hence, the height of the hawk is 462 feet.

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