The angle of elevation from the groud to a bird's nest is 30degrees

LOL CPhill!

Hello helpmeplease,

For this problem, you would use the tangent of 30 degrees. (it is the trig function of opposite/adjacent.)

It helps to first draw out the triangle, which would look something like:

(pretend the nest is at the top of the tree)

You know the angle is 30 deg, and the height is 6. So:

tan(30) = opp/adj

tan(30) = 6/x

Multiply both sides by x.

* tan(30) = 6

Divide both sides by tan(30).

x = 6/ tan(30)

$${\frac{{\mathtt{6}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{30}}^\circ\right)}}} = {\mathtt{10.392\: \!304\: \!845\: \!406\: \!527\: \!5}}$$

So the horizontal distance from the nest to you would be about 10.4 meters:)

Nice pic......

I think you scared the bird off, though.......looks like she took the nest, too....

Breaking news......the bird and nest have been found safe......the mother claims that she temporarily went off on a "tangent"........

Thanks Kitty, but when I do 6/tan 30 on my calculator I get -0.9367

That's not what you got and it doesn't make any sense.

Hello helpmeplease,

That is a common problem with trig functions on calculators. Check that your calculator mode is in degrees, not radians.

Radians are just another way of measuring an angle in pi, so they will show up as small decimal answers.  For most problems you want to use degrees.

On my Ti-84 graphing calculator, I go to "Mode" then go down to the third row and select "Degree" On this site's calculator, you can select "Deg" or "Rad" in the bottom left corner:)

Thank you so much Kitty - I have never heard of radians before.

You're very welcome:) I'm sure your math teacher will explain radians soon.

Breaking news......the bird and nest have been found safe......the mother claims that she temporarily went off on a "tangent".

That's great! I thought the puddy-cat ate the bird.

Yes, i do hope so!  thank you