An observer stands on the edge of a 375 m high cliff. Below him is a river. He estimates that the angle of depression to the near bank of the river is 80° and the angle of depression to the far bank is 60°. Find the width of the river to the nearest metre.

Question

An observer stands on the edge of a 375 m high cliff. Below him is a river. He estimates that the angle of depression to the near bank of the river is 80° and the angle of depression to the far bank is 60°. Find the width of the river to the nearest metre.

Answer 1

In another attempt to determine the height of the flagpole, a metre stick was placed vertically beside the flagpole. When the flagpole’s shadow was 36.72 m long, the metre stick’s shadow was 3.06 m long. Find the height of the flagpole.

Answer 2

First one: triangle

second one: triangle

proportions and trigonometry

Answer 3

h = (36.72m/3.06m) * 1m =

Answer 4

To solve this problem, we can use trigonometry. Let's consider a right triangle with the observer at the top of the cliff, the near bank of the river at the bottom left corner of the triangle, and the far bank at the bottom right corner of the triangle. The height of the cliff is 375 m.

First, let's label the unknown width of the river as "x." Now, we can examine the two angles of depression.

The angle of depression to the near bank is 80 degrees. This means that the angle between the observer's line of sight and the horizontal line is 80 degrees.

The angle of depression to the far bank is 60 degrees. Similarly, this means that the angle between the observer's line of sight and the horizontal line is 60 degrees.

Now, let's use the tangent function to find the width of the river.

For the near bank (angle of depression = 80 degrees):
tan(80) = height of the cliff / width of the river + x

For the far bank (angle of depression = 60 degrees):
tan(60) = height of the cliff / width of the river

Now, we have two equations. Let's solve them simultaneously to find x, the width of the river.

First, let's solve the equation for the near bank:
tan(80) = 375 / (x + width of the river)

Now, let's solve the equation for the far bank:
tan(60) = 375 / x

Rearranging the equations, we have:
(x + width of the river) = 375 / tan(80)
x = 375 / tan(60)

Now, substitute the values of the tangents:
(x + width of the river) = 375 / 5.671
x = 375 / 1.732

Evaluating the values:
(x + width of the river) ≈ 66.05
x ≈ 215.94

Therefore, the width of the river is approximately 216 meters.

Answer 5

Tan 60 = h/d .

Tan 60 = 375/d,
d = ?