Question

A surveyor wants to measure the width of the river from point A to point B. She knows that the distance from a lookout tower at point A to a tree at point C is 115 feet. She uses instruments to measure the angle at A to be 31º. What is the width of the river from point A to point B?

a) 176 feet
b) 207 feet
c) 132 feet
d) 98 feet

Answer 1

To find the width of the river from point A to point B, we can use trigonometry. By solving for the opposite side using the tangent function, we determine that the width is approximately 67.86 feet.

Step-by-step explanation:

To measure the width of the river from point A to point B, we can use trigonometry. Let's consider a right triangle with point A at the vertex, point B at the right angle, and point C as the opposite side of the river. We know that the distance from point A to point C is 115 feet and the angle at point A is 31 degrees.

We can use the trigonometric function tangent to find the width of the river. Tangent is defined as the opposite side divided by the adjacent side. So, we have tan(31 degrees) = width of the river / 115 feet.

Solving for the width of the river, we have width of the river = 115 feet * tan(31 degrees) = 67.86 feet.

Therefore, the width of the river from point A to point B is approximately 67.86 feet.