Can someone explain how to do this, or solve so we can compare answers

From bottom to top

1) green triangle:

cos(28) = 8 / hyp => hyp = 8 / cos(28) = 9.1

2) white triangle:

hyp = 9.1 - 2.5 + 3.6 = 10.2

cos(11) = adj-leg / hyp => adj-leg = hyp*cos(11) = 10.2*cos(11) = 10.0

3) pink triangle:

hyp = 10.0 - 2 + 2.9 = 10.9

(leg)^2 + (3.8)^2 = (10.9)^2 => (leg)^2 = (10.9)^2 - (3.8)^2 = 104.37 => leg = √(104.7) = 10.2

4) blue triangle:

hyp = 10.2 -1 + 3.2 = 12.4

cos(43) = adj-leg / hyp => adj-leg = hyp*cos(43) = 12.4*cos(43) = 9.1

5) dark pink triangle:

leg = 9.1 -1 + 1 = 9.1

cos(30) = leg / hyp => hyp = leg / cos(30) = 9.1 / cos(30) = 10.5

6) light green triangle:

hyp = 10.5 + 3.2 + 1.9 = 15.6

 cos(19) = leg / hyp => leg = hyp*cos(19) = 15.6*cos(19) = 14.8

7) yellow trangle:

leg = 14.8 - 4.8 - 1.1 = 8.9 

cos(46) = leg / hyp => hyp = leg*cos(46) = 8.9*cos(46) = 6.2

8) light purple triangle:

adj-leg = 6.2 + 1.7 = 7.9

hyp^2 = (adj-leg)^2 + (opp-leg)^2 = (7.9)^2 + (3.2)^2 = 72.65 => hyp = 8.5

9) white triangle:

hyp = 8.5 - 2.73 = 5.77

cos(22) =  leg / hyp => leg = hyp*cos(22) = 5.77*cos(22) = 5.35

10) uppest triangle:

leg = 5.35 - 2.24 + 6.9 = 10.01

 cos(4) = leg / hyp => hyp = leg / cos(4) = 10.01 / cos(4) = 10.03

I sugget you work with two decimals (at least) since the begining.

≈ 10.03 cm