Question

2.) According to a Chinese legend from the Han dynasty (206 BCE - 220 ce), General Han Xin flew a

kite over the palace of his enemy to determine the distance between his troops and the enemy
palace. If the general let out 800 meters of string and the kite was flying at a 35° angle of
elevation approximately how far away was the palace from General Han Xin's position?

Answer 1

The palace was 655.32 meters from General Han Xin's position

Explanation:

Let us revise some trigonometry ratios:

• sinФ = opposite side to Ф/hypotenuse
• cosФ = adjacent side to Ф/hypotenuse
• tanФ = opposite side to Ф/adjacent side to Ф

∵ The length of the string is 800 meters

∵ The string represents the hypotenuse for the angle of elevation

∵ The angle of elevation is 35°

- You need the distance between the palace from General

Han Xin's position which it represents the adjacent side

to the angle of elevation, so use the cosine ratio to find

this distance

∵ cos(35) =
`(d)/(800)`

- Multiply both sides by 800

∴ 800 × cos(35) = d

∴ 655.32 ≅ d

∵ d represents the distance between the palace from General

Han Xin's position

∴ The palace was 655.32 meters from General Han Xin's position