Question

One relaxing attraction at the park is a ferry ride across the river. Visitors are picked up at point A and taken across to point B. The return trip drops them off at point C. Find the length of side AB.

Answer 1

To determine the width of the river, we apply trigonometric functions to the right-angled triangle formed by the surveyor's path and use the cosine of the measured angle along with the baseline distance.

Step-by-step explanation:

The student's question involves calculating the width of a river, which is a typical trigonometry problem. In the given scenario, the surveyor creates a right-angled triangle by walking 100 m along the bank and then measuring the angle of 35° to the tree directly across the river. Since we are dealing with a right-angle triangle and we have the angle and the length of the adjacent side (baseline), we can use the trigonometric function cosine (cos) to find the width of the river.

• Let the width of the river be x meters.
• The cosine of angle 35° is equal to the adjacent side (baseline) divided by the hypotenuse (the direct line from the starting point to the tree), which is the width we are looking for.
• Therefore, “cos(35°) = 100 m / x”.
• To find x, we rearrange the equation: x = 100 m / cos(35°).
• We then calculate the value using a calculator equipped with trigonometric functions.

After solving, we will have the width of the river, which is the answer the student is looking for.

Answer 2

If one relaxing attraction at the park is a ferry ride across the river, thus the visitors are picked up at point A and taken across to point B, and the return trip drops them off at point C, then the length of side AB with the endpoints of A is 4,16 and B 20,4 is 7 inches.