Question

the distance between building A and B is 10√3. if the angle of depression to the top and bottom of building B from the top of building A are 30° and 60°.what is the height of building B?​

Answer 1

Explanation:

Let's call the height of building A "hA" and the height of building B "hB". We can use trigonometry to solve for hB.

First, let's draw a diagram:

B

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hB/ |

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/ 60°\

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A

We know that the distance between building A and B is 10√3. Let's call this distance "d".

Using the angle of depression of 30°, we can form a right triangle with a leg of hA and a hypotenuse of d. The opposite angle is 60°, so the adjacent side is hA/tan(60°) = hA/√3.

Using the angle of depression of 60°, we can form another right triangle with a leg of hB and a hypotenuse of d. The opposite angle is 30°, so the adjacent side is hB/tan(30°) = hB√3.

We know that the sum of the heights of building A and B is equal to the distance between them, so hA + hB = d.

Putting all of this together, we can set up an equation:

hA/√3 + hB√3 = 10√3

Multiplying both sides by √3:

hA + 3hB = 30

But we also know that hA + hB = d = 10√3, so we can substitute:

hB = 10√3 - hA

Substituting into the previous equation:

hA + 3(10√3 - hA) = 30

Simplifying:

-2hA + 30√3 = 30

-2hA = 30 - 30√3

hA = (15√3 - 15)/(-1) = 15 - 15√3

Finally, we can use hA + hB = 10√3 to solve for hB:

hB = 10√3 - hA = 10√3 - (15 - 15√3) = 25√3 - 15

Therefore, the height of building B is 25√3 - 15.

Answer 2

the height of building B is 20√3 units.

To solve the problem, we can use trigonometry and create a right triangle with one leg being the height of building B, the other leg being the distance between building A and B, and the hypotenuse being the line of sight from the top of building A to the top of building B.

Let's call the height of building B "h". Using trigonometry, we can determine the length of the other leg:

tan(30°) = h / x => x = h / tan(30°)

tan(60°) = h / (10√3 - x) => x = 10√3 - h / tan(60°)

Setting these two expressions equal to each other and solving for h, we get:

h / tan(30°) = 10√3 - h / tan(60°)

h (1/tan(30°) + 1/tan(60°)) = 10√3

h = 10√3 / (1/tan(30°) + 1/tan(60°)))

Plugging in the values, we get:

h = 10√3 / (1/(1/√3) + 1/√3)

h = 20√3