Question

AOE Find the angle of elevation if you are standing 400 ft. away and the building is 850 ft. tall?

Answer 1

Answer:

64.8°

Step-by-step explanation:

A

Please see attached a rough sketch for your reference

Step one:

Given data

the distance you are standing from the building represent the adjacent =400ft

and the height of the building represents the opposite= 850ft

Step two:

Required is the angle of elevation

applying SOH CAH TOA

Tan ∅= opp/adj

Tan ∅= 850/400

Tan ∅=2.125

∅=Tan-1(2.125)

∅=64.8°

The angle of elevation 64.8°

Answer 2

You can use the fact that buildings are usually standing perpendicular to the ground and ground for smaller distance acts as if its a straight plane.

The measurement of angle of elevation is $64.798^\circ$

What is angle of elevation?

What you see something higher than your eye level height, you need to see up, you elevate your head to see that thing. The angle from the straight horizontal level of eye to the current elevated level is measured and named as angle of elevation.

Similarly, there is angle of depression when the observer looks down.

See the figure attached below to understand the symbols used in calculations.

Since the building is 850 ft tall, we can assume that our height is almost 0 in comparison to this building (the angle deduced then will be approximately equal to the real angle).

Let you're standing on point O

Let the building's base is point A.

Let the top of the building is tagged as point E.

Then we have:

Length of OA = 400 ft.

Length of AE = 850 ft.

To find: angle AOE.

By using the trigonometric ratio tangent, we get:

$tan(\angle AOE) = \dfrac{AE}{OA} = \dfrac{850}{400} = 2.125\\\\ m\angle AOE = arctan(2.125) = 64.798^\circ \text{\: (from calculator)}$

Thus, the measurement of angle of elevation is $64.798^\circ$

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