A girl 160m tall stands 180m from the foot of a building. she find that the angle of elevation of the building is 17 degree. calculate the height of the building to the nearest 1/2 metre

Question

A girl 160m tall stands 180m from the foot of a building. she find that the angle of elevation of the building is 17 degree. calculate the height of the building to the nearest 1/2 metre

Answer 1

Let's call the height of the building "h". We can use the tangent function to set up an equation:

tan(17 degrees) = h / 180m

Now we can solve for "h":

h = 180m * tan(17 degrees)

Using a calculator, we get:

h ≈ 56.8m

Rounding to the nearest 1/2 metre, we get:

h ≈ 57m

So the height of the building is approximately 57m.

Answer 2

To calculate the height of the building, we can use the tangent function.

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

We have the opposite side (O) as 160m (since the girl's height is the opposite side), and the adjacent side (A) as 180m (since the girl is standing 180m from the foot of the building).

The tangent of an angle is defined as the ratio of the opposite side to the adjacent side:

tan(angle) = O / A

Substituting the given values, we have:

tan(17 degrees) = 160 / 180

To solve for H, we rearrange the equation:

H = tan(17 degrees) * A

H = tan(17 degrees) * 180

Calculating this value, we find:

H ≈ 56.32 meters

Therefore, the height of the building to the nearest 1/2 meter is approximately 56.5 meters.

Answer 3

To solve this problem, we can use trigonometry, specifically the tangent function. The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

First, let's define our variables:
H = Height of the building
D = Distance from the girl to the foot of the building
θ = Angle of elevation of the building

We are given:
D = 180m
θ = 17 degrees

Now, we can create a right-angled triangle using the given information. The girl's height, 160m, represents the opposite side, and the distance from the girl to the foot of the building, 180m, represents the adjacent side. We are trying to find the length of the opposite side, which is the height of the building, H.

Using the tangent function, we have the following formula:
tan(θ) = opposite/adjacent

Substituting the known values, we have:
tan(17 degrees) = H/180m

To find H, we can rearrange the equation:
H = 180m * tan(17 degrees)

Now, we can calculate the value:
H ≈ 180m * 0.305
H ≈ 54.9m

Therefore, the height of the building is approximately 54.9 meters.