A surveyor sights the far bank of a river at an angle of 110° to the near bank. She then moves 75 feet upriver and sights the same point on the far bank of the river at an angle of 150°. What is the shortest distance across the river? Please help. Will give brainliest.

Correct answer is 54.82 ft.

Step-by-step explanation:

First of all, let us label the diagram and do the construction as per the attached answer image.

Let us consider :

Let side AB = d ft and let side BC = x ft

We need to find AB to find the shortest distance across the river.

Using trigonometric identity of tangent:

Now, let us have a look at another right angled triangle ABD:

Let us consider :

side AB = d ft and side BD = x+75 ft

Using trigonometric identity of tangent:

Correct answer is 54.82 ft.

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