A man observed that the top of a jar of sugar has an angle of elevation of 30 degrees. After walking 1ft towards the jar, the new angle of elevation is 60 deg

Question

What is the Height of the Jar? 

Answer 1

Michael J. is correct in advising to draw and label a diagram.

In mine A is where you are standing, B is the top of the can, and C is the right angle

m∠A =30°

Draw a line from B to a point on AC and label it D. This is the point 1 foot closer.

m∠BDC = 60°

tan 30° = BC / (DC + 1)

(DC + 1) tan 30° = BC

tan 60° = BC / DC

(DC) tan 60° = BC

(DC + 1) tan 30° = (DC) tan 60°

 

Now solve for DC, return to triangle and solve for BC

Answer 2

You are going to draw a right triangle.  The base angle is 30 degrees with an unknown top angle.  1 ft passed the base angle, draw a line segment to the top angle of the triangle.

 

As a result, you should have two triangles.  An isosceles triangle and a smaller right triangle.  Be sure to label all the angles based on what you know about angle and side relationships.

 

The smaller right triangle contains the height that you need to find.  However, that triangle alone has no known sides.   But, the line segment I told you to draw earlier makes one side of the isosceles triangle and at the same time, the hypotenuse of the smaller right triangle.  Find the length of the segment.  Then you can use trigonometry to find the height using the right triangle.

 

You should get a height of 0.866 ft.