Which of the following is associated with the famous impossible Delian problem?

1 answer:

8 0

THE ANSWER ABOVE IS INCORRECT!! If you are doing Apex, the answer is doubling a cube. It can't be done with a straightedge or compass so it is impossible and was believed to be Apollo wanted something of his doubled with was a cube.

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From a balloon 1191 feet high, the angle of depression to the ranger headquarters is 72°54'. How far is the headquarters from a

Volgvan

If you take a look at my really poorly drawn diagram, we can see it is a trigonometry problem. The angle, however, is outside the triangle, and we can find the angle inside the triangle next to it by taking it away from 90°:
90°0' - 72°54' = 17°6' ≈ 17.1°.
We can find the other angles becuase one is 90° and the other is:
180°-90°-17°6'=72°54' ≈ 72.9°(which you can see if you know your angle theorems).

We now have diagram 2, nicely simplified so we can see where to go.
Using the Sine Rule, i.e.
$\frac{sin(A)}{a} = \frac{sin(B)}{b}$
We can rearrange to find our length b:
$b=a \frac{sinB}{sinA}$
Substituting numbers in:
$b=1191 \frac{sin(17.1)}{sin(72.9)} =366.399...ft$
b=366 feet.