A surveyor is measuring the width of a pond. She chooses a landmark on the opposite side of the pond, and measures the angle to this landmark from a point 50 feet away from the original point. How wide is the pond to the nearest ft?

Step 1: Identify the given information and the unknown. The problem describes a right-angled triangle ABC, where the right angle is at B. The length of side BC is given as 50 ft. The width of the pond is represented by the side AB. From the faint writing on the image, we assume the angle BCA = 70^. Step 2: Choose the appropriate trigonometric ratio. In a right-angled triangle, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. For angle C, the opposite side is AB and the adjacent side is BC. ( BCA) = oppositeadjacent = (AB)/(BC) Step 3: Substitute the known values into the formula. We have BCA = 70^ and BC = 50 ft. (70^) = (AB)/(50) Step 4: Solve for AB. Multiply both sides by 50 to find AB. AB = 50 × (70^) Step 5: Calculate the value and round to the nearest foot. Using a calculator for (70^): (70^) ≈ 2.747477 AB = 50 × 2.747477 AB ≈ 137.37385 Rounding to the nearest foot: AB ≈ 137 ft The width of the pond is approximately 137 ft. The width of the pond is 137 ft. Send me the next one 📸