Answer
The value for q=6.1 and the value for r=7.9.
Work Step by Step
This is a two-step problem as q and r must be found separately and then added together.
Solving for q comes first because it allows us to solve for r using the same length of the base.
Using the tan rule of opposite/base, the equation is modelled as $ tan17 = \frac{q}{20} $ . Multipling 20 to both sides will isolate q and give us an equation of $ tan17 * 20 = q $. Plugging in 0.305 for tan17 and simplfiying, we get a result of q=6.1.
Solving for r uses the same idea of opposite/base. We add both angles of 17 and 18 to obtain the angle necessary for r, which is 35. The opposite length in this case is q+r. Since we already know q, the equation can be shown as $tan35 = (6.1 + r)/20 $. Multiplying both sides by 20 and simplifying for the left side will give us an equation of $ 14 = 6.1 + r $. Subtracting the 6.1 from the 14 then solves for r, which is 7.9.
