High School

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From the top of a cliff 92.9 m above a stream, the angle of depression to a point on the near shore is 48.5 degrees, and to a point on the far shore is 37.9 degrees.

Find the width of the stream between these two points.

Answer :

Answer:

37,15m

Step-by-step explanation:

the distance between top of the cliff to the ground at shore level

and the distance between the top of the clif to the stream shore

defines a triangle rectangle.

Where: [tex]Tan(\alpha )=\frac{opossite side}{adjacent side}=\frac{x}{y} \\[/tex]

x= distance from shore to bottom of the cliff

y= distance from top of the cliff to the bottom of the cliff

[tex]y*tan(\alpha)=x\\[/tex]

α1= 90°-48,5°= 41,5°

α2=90°-37,9°= 52,1°

x1= distance between near shore to the bottom of the cliff

x2= distance between far shore to the bottom of the cliff

[tex]x1=y*tan(\alpha1)=92,9m*tan(41,5°) \\[/tex]

[tex]x2=92,9m*tan(52,1°)[/tex]

[tex]x2-x1=y*tan(\alpha2)-y*tan(\alpha1)[/tex]

[tex]x2-x1=119,34°-82,19°[/tex]

distance= 37,15°

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