Jan is standing 2 m in front of a painting on a wall. The bottom frame of the painting is 1.4 m from the floor, and Jan is 165 cm tall. The painting has a height of 70 cm.

Question

1. a  Draw a diagram to show this

   information.

2. b  Find the angle of elevation from

   Jan’s eyes to the top frame of the

   painting.

3. c  What is the angle of depression from

   Jan’s eyes to the bottom frame?

4. d  If Jan stood 1 m further away from the painting, through what angle

   would she have to sweep her eyes to view from the top to the bottom frame?

Answer 1

a) diagram https://ibb.co/v1BxzrW

b) BC = BF - AE = 0.5m

And AC = 2m

So, tan BAC = BC/AC = 0.5/2

or <BAC = tan^-1 (0.5/2) = 14.04 degrees

c) CD = AE- DF = 0.2m

AC = 2m

So, tan DAC = CD /AC = 0.2/2

or <DAC = tan^-1 (0.2/2) = 5.7 degrees

d) diagram: https://ibb.co/d66XYJ8

BC = 0.5 and CD = 0.2 and AC=1

tan BAC = BC/AC = 0.5

<BAC = tan^-1 (0.5) = 26.57 degrees

tan DAC = CD/AC = 0.2

<DAC = tan^-1(0.2) = 11.31 degrees

So the sweeping angle = <BAC + <DAC = 26.57+11.31 = 37.88 degrees