Answer:
8.4 cm
Step-by-step explanation:
The sides involved are opposite and adjacent to the given angle. Therefore, you should use the tangent ratio.
Substitute:
tanx = opp/adj
tan35 = x/12
Multiply by 12 on both sides:
12(tan35) = (x/12)12
12(tan35) = x
Solve:
12(tan35) = x
8.4 = x
Simplify both sides if needed. The left-hand side needs simplification.
4(x - 6)

-2x + 6
4x - 24

-2x + 6
All is left to do is add and subtract to get the x variable all alone.
4x - 24

-2x + 6
6x - 24

6 <-- Add 2x to both sides
6x

30 <-- Add 24 to both sides
x

5 <-- Divide both sides by 6
In order to be in the solution set, x has to be less than or equal to 5.
In interval notation: [5, -∞)
Triangles CPA and CPB are both right triangles. They share a leg, so that leg in one triangle is congruent to that leg in the other triangle. We are given that PA is congruent to PB by the hash marks on the diagram. Thus two legs and an included angle are congruent between the triangles.
... ∆CPA ≅ ∆CPB by the SAS postulate
Then side CA ≅ CB = 15 in, because corresponding parts of congruent triangles are congruent (CPCTC).
... CA is 15 in.
[ 2x + y = -9 ] x -3
[- 3x +11= y ] x 2
-6x -3y = 27
-6x + 22 = 2y
-6x +27 = 3y
-6x +22 = 2y
5 = y
-6x -3x5 = 27
-6x -15 = 27
-6x = 42
-x = 42/6
-x = 7
x = -7
answer
x = -7
y = 5