Question

Please help me! Thank you!

Answer 1

Answer:p = 28.36

q = 31.78

Step-by-step explanation:

Considering the smaller right angle triangle, with 50° as the reference angle, the opposite side is q and the adjacent side is 55 - p

Applying the tangent trigonometric ratio which is expressed as

Tan θ = opposite side/adjacent side

Tan 50 = q/(55 - p)

1.1918(55 - p) = q - - - - - - - - - 1

Considering the bigger right angle triangle, with 30° as the reference angle, the opposite side is q and the adjacent side is 55

Applying the tangent trigonometric ratio which is expressed as

Tan θ = opposite side/adjacent side

Tan 30 = q/55

0.5774 = q/55

q = 55 × 0.5774

q = 31.757

Substituting q = 31.757 into equation 1, it becomes

1.1918(55 - p) = 31.757

65.549 - 1.1918p = 31.757

1.1918p = 65.549 - 31.757

1.1918p = 33.792

p = 33.792/1.1918

p = 28.36