Question

A large totem pole near Kalama, Washington is 130ft tall. On a particular day at noon it cast a 180ft shadow. What is the sun's angle of elevation at that time?

Answer 1

A large totem pole near Kalama, Washington is 130ft tall. On a particular day at noon it cast a 180ft shadow. What is the sun's angle of elevation at that time?

Solution.

The angle of elevation is how high the sun is. In our case the angle is $\varphi$ . To find $\varphi$ we should use trigonometric formulas and write an equation:

$$t g \varphi = \frac {A C}{A B} = \frac {1 3 0}{1 8 0} = \frac {1 3}{1 8}$$ $$\varphi = \operatorname {a r c t g} \left(\frac {1 3}{1 8}\right) \approx 3 5. 8 {}^ {\circ}$$

Answer: $35.8{}^{\circ}$