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
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).
To find the height of the kite, we can use trigonometry. Let's consider the triangle formed by the observer at point P, the kite, and its height.
From the observer at point P, we have an angle of elevation of 35°. This means that the angle between the observer's line of sight and the horizontal ground is 90° - 35° = 55°.
Similarly, from the observer at point Q, we have an angle of elevation of 45°. This means that the angle between the observer's line of sight and the horizontal ground is 90° - 45° = 45°.
Now, let's consider the triangle formed by the kite and the observer at point P. We can label the height of the kite as h (which we need to find), the distance between the observer at point P and the kite as x (15m), and the angle between the line connecting the observer at point P and the kite and the horizontal ground as α (55°).
Using trigonometry, we can write the equation:
tan(α) = h/x
tan(55°) = h/15
h = 15 * tan(55°)
Calculating this, we find:
h ≈ 21.54 meters
Therefore, the height of the kite is approximately 21.54 meters to the nearest meter.