Question

The real estate agent is trying to figure out the width of the lot for sale. He first stands at point D, directly opposite point E. He then walked 1800 feet to point F. He measures the acute angle at point F to be 79 degrees. What is the width, w, of the lot? If necessary, round to the nearest tenth.

Answer 1

To solve this problem, we can use trigonometry and specifically focus on the concept of a right triangle.

Let's assume that point E represents one end of the lot, point F represents the location where the agent stands after walking 1800 feet, and point D represents the other end of the lot. We can consider line segment DE as the width of the lot.

Since the agent is standing directly opposite point E at point D, we can form a right triangle DEF. The line segment DF represents the hypotenuse of the triangle, and the acute angle at point F is given as 79 degrees.

Now, we can use trigonometric functions, specifically the cosine function, to find the width (DE) of the lot. The cosine of an angle in a right triangle is equal to the adjacent side divided by the hypotenuse.

cos(79 degrees) = DE / DF

Since the agent walked 1800 feet to reach point F, we have:

cos(79 degrees) = DE / 1800

To find DE, we rearrange the equation:

DE = 1800 * cos(79 degrees)

Calculating the value:

DE ≈ 1800 * 0.2040 ≈ 367.2

Therefore, the width of the lot, rounded to the nearest tenth, is approximately 367.2 feet.