Question

You are standing 41 meters from the base of a building. You estimate that the angle of elevation to the top of the 86th floor (the observatory) is 82°. If the total height of the building is another 124 meters above the 86th floor, what is the approximate height of the building? (Round your answers to one decimal place.)

Answer 1

Answer:

408.6 meters.

Step-by-step explanation:

Let x be the height from the base of the building to the 86th floor,

∵ the total height of the building is another 124 meters above the 86th floor,

So, the total height of the building = ( x + 124 ) meters,

Now, the angle of elevation from the point on the ground to 86th floor = 82°,

Also, the distance from the point to the base of the building = 41 meters,

Thus, by trigonometric ratio,

$tan 82^{\circ}=\frac{x}{41}$

$\implies x = 41\times tan 82^{\circ}=284.614788895\approx 284.6\text{ meters}$

Hence, the height of the building = ( 284.6 + 124 ) = 408.6 meters.

Answer 2

The height of the building in consideration is given approximately as 408.61 meters

What is angle of elevation?

You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.

Consider the figure attached for the given situation as described in the problem.

The person watching the building's 86th floor is at A.

The 86th floor is at C, the base of the building is at B.
The total height of the building is at D.

Using the tangent ratio to find the height of the building, we get:

$\tan(82^\circ) = \dfrac{x}{41} \\\\x = \tan(82^\circ) \times 41\\x \approx 284.61 \: \rm meters$ (from calculator).

Thus, the height of the building is length of AD

= |AD| = x + 124 ≈ 284.61 + 124 = 408.61 meters

Thus, the height of the building in consideration is given approximately as 408.61 meters

Learn more about tangent ratio here:

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