Question

Amari is standing 50 feet from the base of a building. From where he stands, the angle formed between the top of the building and the ground at his feet is 60°. Amari is standing 50 feet from the base of a building. From where he stands, the angle formed between the top of the building and the ground at his feet is 60 degrees. The angle between the building and the ground is a right angle. How tall is the building? 50 ft StartFraction 50 StartRoot 3 EndRoot Over 3 EndFraction ft 50 StartRoot 3 EndRoot ft 100 ft.

Answer 1

Answer:

86.6 feet

Step-by-step explanation:

this could be represent as a triangle (as shown in the image)

The red rectangle is the building

the green person is Amari

So we use the (soh cah toa) to solve this

and specifically the (toa) which mean tan=opposite/adjacent

the opposite is the side that been directly in the opposite of the angle and in this case is equal to the tall of the building

the adjacent is the side that near the angle (and not the hypotenuse) and in this case is equal 50 feet

tan60 = opposite/50

tan60 = opposite/50

√3 = opposite/50

opposite = 50√3

opposite = 86.6 feet

the tall of the building = 86.6 feet

Answer 2

The height of the building is 50√3 feet.

Given to us,

Distance between the building and Amar = 50 feet,

Angle between the top of the building and Amar = 60°

We know that the value of tan 60° is √3.

Thus,

$tan\theta=\dfrac{Perpendicular}{Base} \\\\\rm tan\ 60^o =\dfrac{Height\ of\ the\ building}{Distance\ between\ building\ and\ Amar}$

$\sqrt{3} =\dfrac{Height\ of\ the\ building}{50\ feet}$

${Height\ of\ the\ building}= {50\ feet}\times\sqrt{3}$

Therefore, the height of the building is 50√3 feet.

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