what is the angle of elevation of the sun when a tree 6.25m tall casts a shadow 10.1m long?

Question

 Can you please show me the work needed to get this answer and what trig function did you use. 

Answer 1

JT,

I can lead you partway. Draw the triangle, with the short tree standing straight up on the left, the long shadow as a horizontal length from the tree to the right, and a hypotenuse.

 

The trig functions are defined in terms of three sides: opposite, adjacent, and hypotenuse.

 

You know two numbers, let’s figure which sides they are.

So put your finger on the sharp point of the triangle. That’s the angle of elevation. 

 

The height of the tree is which side? (Opposite, adjacent, or hypotenuse)

 

The length of the shadow is which side?

 

The trig functions are

sine , which is opposite/hypotenuse

cosine, adjacent / hypotenuse

tangent, opposite / adjacent

 

You have numbers for two of those sides. Which two? Which function deals with those two sides?

 

The tree height is opposite

The shadow length is adjacent

the formula that relates opposite to adjacent is tangent.

 

so you want the angle that has tangent of 6.25/10.1

 

this is written as tan^-1(6.25/10.1)

a spreadsheet or software program has either atan() or arctan().

 

so, do the arithmetic, and then look up the tangent.