You can solve x+30+90 = 180 or you can solve x+30 = 90 to find that x = 60. Note how angle PTR and angle TPR are complementary angles. A shortcut is to do 90-30 = 60.
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Part B
The exact length of PR is 7 inches
Triangle TPR is a 30-60-90 triangle, so the short leg is half that of the hypotenuse (14). Take half of 14 to get 7. The short leg is always opposite the 30 degree angle for a 30-60-90 triangle.
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Part C
Answer: 7*sqrt(3) The notation "sqrt" is shorthand for "square root"
TR is the long leg of the right triangle TPR. The long leg of a 30-60-90 triangle is equal to sqrt(3) times the short leg. Alternatively, you can use the pythagorean theorem to solve for the long leg.
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Part D
Answer: 7*sqrt(2)
Triangle PRQ is a right triangle. It is a 45-45-90 right triangle. The hypotenuse is equal to sqrt(2) times the leg 7. Alternatively, you can use the pythagorean theorem to solve for the hypotenuse.
