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surveyor wishes to measure the distance across a stream. He sets up his transit
at a point C on the bank of the stream, and sights on a point B on the other
bank directly opposite him. Then he turns the transit through a right angle
and measures off a distance of 100 feet to a point A. He moves the transit to
A, and measures the angle CAB, which he finds to be 50°. How wide is the
stream?

Sagot :

Abidemiokinidn

According to the information given, the width of the stream is 119.18 feet

Find the diagrammatic representation shown;

From the figure, we can see that:

  • Width of the stream = BC
  • m<CAB = 50 degrees
  • AB = 100 feet

Using the SOH, CAH, TOA identity

[tex]tan \ m \angle CAB=\frac{opposite}{adjacent}\\ tan \ m \angle CAB=\frac{CB}{AB}\\tan \ 50= \frac{x}{100}\\x=100tan 50\\x= 100(1.1918)\\x=119.18feet[/tex]

This shows that the width of the stream is 119.18 feet

Learn more here: https://brainly.com/question/14374661

View image Abidemiokin
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