Question

Find the value of p and q

Answer 1

Answers:  p = 28.36,  q = 31.75

values are approximate & rounded to 2 decimal places

===================================================

Work Shown:

tan(angle) = opposite/adjacent

tan(30) = q/55

q = 55*tan(30)

q = 31.7542648054294

q = 31.75

--------

r = 55-p

tan(angle) = opposite/adjacent

tan(50) = q/(55-p)

tan(50) = q/r

tan(50) = 31.7542648054294/r

r*tan(50) = 31.7542648054294

r = 31.7542648054294/tan(50)

r = 26.6449918865414

55-p = 26.6449918865414

-p = 26.6449918865414-55

-p = -28.3550081134586

p = 28.3550081134586

p = 28.36

Answer 2

Answer:

The answer to your question is p =  27.7      q = 29

Step-by-step explanation:

Process

1.- Calculate the value of all the angles of the triangle

The angle of 50° and the one to the right are supplementary

                                   x + 50 = 180

                                   x = 130°

- The sum of the internal angles in a triangle equals 180°

                     30° + y + 130° = 180

                              y = 180 - 130 - 30

                              y = 180 - 160

                              y = 20°

- The angle of the right triangle

                     50 + 90 + z = 180

                              z = 180 - 90 - 50

                              z = 40°

If sum up the superior angles 20 + 40 = 60°, then the biggest triangle is a 30-60-90

2.- Calculate q using the trigonometric function tangent

                        tan Ф = q / 55

solve for q

                        q = 55 tan 30

                         q = 28.9 ≈ 29

3.-  Calculate the hypotenuse of the biggest triangle

                       h² = 55² + 29²

                       h² = 3866

                       h = 62,12

4.- Use law of sines to find p

                     $\frac{p}{sin 20} = \frac{62.12}{sin 130}$

solve for p

                       p = $\frac{62.12 sin 20}{sin 130}$

                       p = 27.74