Question

From a distance of 1217 feet from a spotlight,the angle of elevation to a cloud base is 43 degrees. Find the height of the cloud base to the cloud base to the nearest foot

Answer 1

Using the tangent function with a given distance of 1217 feet and an angle of elevation of 43 degrees, the height of the cloud base is calculated to be approximately 1136 feet to the nearest foot.

Step-by-step explanation:

To find the height of the cloud base given the distance to the spotlight and the angle of elevation, we can use trigonometric functions. Specifically, we will use the tangent function, which relates the angle of elevation to the ratio of the opposite side (height of the cloud base) to the adjacent side (distance from the spotlight).

The formula we use is:

height = distance × tan(angle of elevation)

We are given:

• Distance = 1217 feet
• Angle of elevation = 43 degrees

We will calculate the height as follows:

height = 1217 × tan(43 degrees)

Using a calculator, we find that:

height ≈ 1217 × 0.932515 (tan(43 degrees) ≈ 0.932515)

height ≈ 1135.64 feet

To the nearest foot, the height of the cloud base is approximately 1136 feet.

Answer 2

1134.9 ft

Step-by-step explanation:

CHECK THE ATTACHMENT FOR THE FIQURE

From, trigonometry,

Tan(X) = opposite/ adjacent

Distance from the spotlight = 1217 ft, which is the adjacent sides

Let the height of the cloud= X

, Which is the opposite sides

Then substitute, we have

Tan(43°)= X/1217

(0.9325)= X/1217

X= 0.9325×1217

= 1134.9 ft

Hence, the height of the cloud base to the cloud base to the nearest foot is 1134.9 ft