Question

A student measures the angle of elevation of a building from two different points.from point p and q.he finds that the angle of elevation of the top of the building to be 37° and 58° respectively.if the distance between p and q is 48m, calculate the height ot the building correct to 3 significant figure

Answer 1

Answer:

The height of the building is approximately 44.8 meters (to 3 significant figures).

Step-by-step explanation:

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

From point P, the angle of elevation of the top of the building is 37°. This means that the height of the building (h) is given by:

h = x * tan(37°)

where x is the distance between point P and the building. We don't know the value of x yet, but we can use the information from point Q to find it.

From point Q, the angle of elevation of the top of the building is 58°. This means that the height of the building (h) is given by:

h = y * tan(58°)

where y is the distance between point Q and the building.

We know that the distance between point P and Q is 48m. Therefore, we can express x in terms of y as follows:

x + y = 48

x = 48 - y

Now we can substitute x into the first equation to get:

h = (48 - y) * tan(37°)

And we can substitute y into the second equation to get:

h = y * tan(58°)

Since both equations give the same value for the height of the building (h), we can equate them:

(48 - y) * tan(37°) = y * tan(58°)

Solving for y, we get:

y = 28.14 meters

Substituting y back into either equation, we get:

h = y * tan(58°) = 44.84 meters

Therefore, the height of the building is approximately 44.8 meters (to 3 significant figures).

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