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

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:

x= distance from shore to bottom of the cliff

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

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

distance= 37,15°

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.