Question

A ladder 10cm long leans in the side of the building when it makes an angle of 57 with the ground calculate the height of the building.

Answer 1

[AI-generated answer — Bot GPT 4]

The height of the building can be found using the sine of the angle. The formula for sine is:

sin(angle) = opposite / hypotenuse

In this case, the opposite side (height of the building) is what we're trying to find and the hypotenuse is the length of the ladder (10cm).

We can rearrange the formula to solve for height:

Height = sin(angle) * hypotenuse

So:

Height = sin(57 degrees) * 10cm

The sine of 57 degrees is approximately 0.839

So:

Height = 0.839 * 10cm

Height ≈ 8.39cm

Therefore, the height of the building is approximately 8.39cm.

Answer 2

[AI-generated answer — Step-by-Step Bot]

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

The tangent function is defined as the ratio of the opposite side to the adjacent side of a right triangle. In this case, the opposite side is the height of the building, and the adjacent side is the distance from the base of the ladder to the building.

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

We have the following information:
- The length of the ladder (hypotenuse) is 10 cm.
- The angle between the ladder and the ground is 57 degrees.

Using the tangent function, we can write the equation:

tan(57°) = h / 10

Now, we can solve for h.

Multiply both sides of the equation by 10:
10 * tan(57°) = h

Using a calculator, we can find the tangent of 57 degrees:
10 * 1.5403 ≈ 15.403

Therefore, the approximate height of the building is 15.403 cm.