2. A surveyor measures the distance across a river that flows straight north by the following method. Starting directly across from a tree on the opposite bank, the surveyor walks 100 m along the river to establish a baseline. She then sights across to the tree and reads that the angle from the baseline to the tree is 35°. How wide is the river?

Question

Victoria Carey

Mathematics

14 December, 12:03

2. A surveyor measures the distance across a river that flows straight north by the following method. Starting directly across from a tree on the opposite bank, the surveyor walks 100 m along the river to establish a baseline. She then sights across to the tree and reads that the angle from the baseline to the tree is 35°. How wide is the river?

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Answers (1)

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Avery Curtis · Answer 1

The wide is 70.02 m.

Step-by-step explanation:

First you need to draw a triangle with only one 90 degrees angle.

The opposite side to the 90 degrees angle will be the hypotenuse.

We will call the remaining sides ''Baseline'' and ''River wide''.

The angle between hypotenuse and baseline is 35 degrees.

The triangle has one 90 degrees angle so we can apply the tangent equation

in the angles that are no 90 degrees.

Tangent (angle) = Opposite side/adjacent

Tan (35°) = River wide/100m

River wide = 100m. Tan (35°)

River wide = 70.02 m