Two observe p and q.15m apart observe a kite in a vertical plane and from the same side of the kite . the angle of elevation of the kite from p and q are 35°and45° respectively.find the height of the kite to the nearest metre

Answer 1

Let the height of the kite be h meters.
From triangle PAK, we have:

tan 35° = h / PK

From triangle QA'K, we have:

tan 45° = h / QA'

Since PK + QA' = 15m, we can rearrange the second equation to get:

QA' = 15 - PK

Now substitute PK from the first equation into the second equation:

tan 45° = h / (15 - tan 35° * PK)

Simplifying this equation, we get:

h = (15 - tan 35° * PK) * tan 45°

We can solve for PK by using the first equation and rearranging to get:

PK = h / tan 35°

Substituting this into the equation for h, we get:

h = (15 - h / tan 35° * tan 45°) * tan 45°

Simplifying this equation, we get:

h = 15 * tan 45° / (tan 45° + tan 35°)

Plugging in the values, we get:

h = 20.69 meters

Therefore, the height of the kite is approximately 21 meters (to the nearest meter).