Question

An observer (O) is located 500 feet from a school (S). The observer notices a bird (B) flying at a 39° angle of elevation from his line of sight. What equation and trigonometric function can be used to solve for the height (h) of the bird? Pick another trigonometric function and describe why that function is not appropriate when trying to solve for (h).

WILL GIVE MEDAL

Answer 1

We know the side adjacent to the angle and we want to know the opposite side. Which of trig functions relates the opposite and adjacent sides?

Answer 2

http://www.mathwarehouse.com/trigonometry/images/sohcohtoa/sohcahtoa-all.png <--- recall soh cah toa

so which one do you think we could use for that?

we know the adjacent, we need the opposite?

Answer 3

tangent

Answer 4

yes. and that means you say
tangent (angle) = opp/adj

Answer 5

Yes. \[tan(\theta)=\frac{opposite}{adjacent}\]

Answer 6

so now what do we do with that

Answer 7

fill in the parts you know

Answer 8

\(\bf tan(\theta)=\cfrac{opposite}{adjacent}\implies tan(39^o)=\cfrac{h}{500}\implies 500\cdot tan(39^o)=h\)

Answer 9

so h = 500tan(39) ?

Answer 10

yeap

Answer 11

can you simplify that

Answer 12

you can change it to a decimal number (using a calculator), but the exact answer can only be written that way.