A surveyor needs to determine the distance across the pond shown in the accompanying diagram . She determines that the distance from her position to point P on the south short of the pond is 175 meters and the angle from her position to point on the north shore is 32 degrees . Determine he distance , PX, across the pond , rounded to the nearest meter .

Question

A surveyor needs to determine the distance across the pond shown in the accompanying diagram . She determines that the distance from her position to point P on the south short of the pond is 175 meters and the angle from her position to point on the north shore is 32 degrees . Determine he distance , PX, across the pond , rounded to the nearest meter .

Answer 1

Need a description of the pond, where is X ?

Answer 2

To determine the distance PX across the pond, we can use basic trigonometry principles. We are given the distance from the surveyor's position to point P on the south shore of the pond, which is 175 meters, and the angle from the surveyor's position to point X on the north shore of the pond, which is 32 degrees.

In the diagram, the surveyor's position is marked as S, point P on the south shore is marked as P, and point X on the north shore is marked as X. The distance across the pond, PX, is the unknown length we want to find.

To solve the problem, we will use the trigonometric function tangent since we know the opposite side (PX) and the adjacent side (SP). The tangent function is defined as the ratio of the opposite side to the adjacent side in a right triangle.

Step 1: Identify the right triangle
In this case, we can form a right triangle by connecting points S, P, and X.

Step 2: Identify the sides of the right triangle
In the right triangle, the side opposite to the angle is PX, which we want to find. The side adjacent to the angle is SP, given as 175 meters.

Step 3: Apply the tangent function
Tangent(theta) = opposite / adjacent

In this case, we have:
Tangent(32 degrees) = PX / 175

Step 4: Solve for PX
Rearranging the equation, we have:
PX = Tangent(32 degrees) * 175

Now, we just need to calculate the value of Tangent(32 degrees) and multiply it by 175 to find PX.

Using a scientific calculator or an online calculator, we can find that Tangent(32 degrees) is approximately 0.6249.

Substituting the value into the equation:
PX = 0.6249 * 175

Calculating this, we get:
PX ≈ 109.36 meters.

So, rounding to the nearest meter, the distance PX across the pond is approximately 109 meters.

Answer 3

If we label the surveyor as point S, all we have is one angle and one side.

Unless you can provide some information about another angle or side, we're stuck.