Your search for A surveyor is trying to determine the width of a river. He forst stands at point A, directly opposite a tree at point B. He then walks 100 feet to point C. He measures the acute angle at point C to be 79 degrees. What is the width of the river?
w/100 = tan 79°
36
To determine the width of the river, we can use trigonometry and the information given in the problem.
Let's assume that the width of the river is represented by the line segment BD, where D is the point at which the surveyor is standing. We need to find the length of BD.
From the given information, we know that the surveyor first stands at point A, directly opposite the tree at point B. This implies that AB is perpendicular to BD.
Next, the surveyor walks 100 feet to point C and measures the acute angle at point C to be 79 degrees. This information allows us to use trigonometry to find the length of BD.
1. Start by drawing a diagram to visualize the situation. Label the points as described: A, B, C, and D.
2. Identify the right triangle ABC, where the right angle is at point B.
3. Recall that in a right triangle, the sine function relates the opposite side length to the hypotenuse length. In this case, we are interested in the length of BC, which is the opposite side to the angle 79 degrees. Let's call the length of BC x.
4. Apply the sine function:
sin(79°) = BC / AB
sin(79°) = x / 100
5. Solve for x (BC):
x = 100 * sin(79°)
6. Calculate the value of x using a calculator or a trigonometric table.
7. Once you have the value of x, you have determined the length of BC, which represents the width of the river (BD).
So, by following these steps, you can find the width of the river using trigonometry based on the measurements and angles provided in the problem.
think twice, type once...
100/w = tan 79°