Question

iron man is flying at an attitude of 30km. Pepper is at a surface distance of 12km from his location. what is the angle of elevation when she looks up to see him?

Answer 1

We will solve as follows:

The shape is a rectangle triangle with a side of 30 and other side of 12. We calculate the hypotenuse:

$h=\sqrt[]{12^2+30^2}\Rightarrow h=6\sqrt[]{29}$

Now, using the law of sines, we solve:

$\frac{6\sqrt[]{29}}{\sin(90)}=\frac{30}{\sin (\alpha)}$

Now we solve for alpha:

$\Rightarrow\sin (\alpha)=\frac{30\sin(90)}{6\sqrt[]{29}}\Rightarrow\alpha=\sin ^{-1}(\frac{30\sin(90)}{6\sqrt[]{29}})$

From this we will have that the angle of elevation when she looks is of aproximately 68.2°.