MATH SOLVE

3 months ago

Q:
# 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

Accepted Solution

A:

Answer:37,15mStep-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 shoredefines a triangle rectangle.Where: [tex]Tan(\alpha )=\frac{opossite side}{adjacent side}=\frac{x}{y} \\[/tex]x= distance from shore to bottom of the cliffy= 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 cliffx2= 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°