Two observers on opposite sides are 350m apart and are looking at a balloon if the angles of elevation from each observer are 30degree and 60degree respectively,how high is the balloon?

Question

Two observers on opposite sides are 350m apart and are looking at a balloon if the angles of elevation from each observer are 30degree and 60degree respectively,how high is the balloon?

Answer 1

make your sketch

let the point below the ballon be P
let the distance from the 60° position to P be x
then the other distance is 350-x

You have two right-angled triangles
let the height be h m (the common side to the two triangles)

for the 1st triangle:
tan60 = h/x
h = xtan60

for the 2nd:
tan30 = h/(350-x)
h = (350-x)tan30
so
xtan60 = (350-x)tan30
xtan60 = 350tan30 - xtan30
xtan60 + xtan30 = 350tan30
x(tan60 + tan30) = 350tan30
x = 350tan30/(tan60+tan30)

back to the 1st triangle
h = xtan60

h = 350tan30tan60/(tan60+tan30)
= ...
Only now would I reach for my calculator and do all the calculations in one swoop using the ( ) keys to make sure of my order of operations.

I got appr 151.55 m

Answer 2

thank you sir it is really helpful :)

Answer 3

To find the height of the balloon, we can use trigonometry.

Let's assume that the height of the balloon is h meters.

From the first observer's perspective, the angle of elevation to the balloon is 30 degrees. This means that the opposite side to this angle is equal to the height of the balloon, h. The adjacent side is the distance between the observer and the balloon, 350m.

Using the tangent function, we can set up the following equation:

tan(30°) = h / 350

Simplifying this equation, we get:

h = 350 * tan(30°)

Calculating this value, we find:

h ≈ 350 * 0.577
h ≈ 201.95 meters

Therefore, the height of the balloon is approximately 201.95 meters.

Answer 4

To find the height of the balloon, we can make use of trigonometry. Let's consider Observer A and Observer B.

First, let's draw a triangle to represent the situation. The distance between the two observers (Observer A and Observer B) can be represented as the base of the triangle, and the height of the balloon can be represented as the vertical side of the triangle.

Let's denote the height of the balloon as 'h'.

Now, we have two angles of elevation: 30 degrees for Observer A and 60 degrees for Observer B.

Looking at Observer A:

In triangle AOB (where O is the position of the balloon), we have one known side (OB = 350m) and one known angle (angle AOB = 30 degrees).

Using trigonometry, we can use the tangent function to find the height of the balloon from Observer A:

tan(30 degrees) = h / 350

Solving this equation for 'h', we have:

h = 350 * tan(30 degrees)

Now, let's calculate this value.

tan(30 degrees) can be found using a scientific calculator or table, and its approximate value is 0.577.

Therefore, the height from Observer A is:

h = 350 * 0.577
h ≈ 201.95 meters

Next, let's calculate the height of the balloon from Observer B.

In triangle AOB, we have one known side (OA = 350m) and one known angle (angle OBA = 60 degrees).

Using trigonometry again, we can use the tangent function to find the height of the balloon from Observer B:

tan(60 degrees) = h / 350

Solving this equation for 'h', we have:

h = 350 * tan(60 degrees)

Now, let's calculate this value.

tan(60 degrees) can be found using a scientific calculator or table, and its approximate value is 1.732.

Therefore, the height from Observer B is:

h = 350 * 1.732
h ≈ 606.2 meters

So, the height of the balloon is approximately 606.2 meters when observed from Observer B.