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GOAL: To design the plans to rebuild a skateboard ramp that was damaged by vandalism

Its an acute triangle with Sides A,B,C, and D. Ill attempt to make it..
                                   /  B  |     \
                               /          |        \
                           /              |             \
                       /                  |10 ft            \    
                   /                      |                      \
              /                           |                          \
              ______________90|_________________30 degrees     
         A                          D                                         C
                        5ft     


GOAL: To design the plans to rebuild a skateboard ramp that was damaged by vandalism.

ROLE: You, being the engineer on the project, need to find all missing dimensions on the triangles in the image. This includes all missing sides and angles in each right triangle. This is also known as "Solving the Triangles".

AUDIENCE: The poor skateboarders that keep falling on the destroyed ramp and the construction crew that is going to do the actual rebuilding. The crew is waiting on the plans.

SITUATION: Use the skills you have learned about the Pythagorean theorem, special right triangles, and trigonometric ratios to find every missing side and every missing angle in each triangle in the image.

PERFORMANCE: Accurately calculate, to the nearest tenth, the missing sides and three missing angles in each of the triangles. Show all of your work and calculations for each missing side or angle. Explain in complete sentences all of your steps and display the answers in the correct units.
 

GOAL:  To design the plans to rebuild a skateboard ramp that was damaged by vandalism.

ROLE:  You, being the engineer on the project, need to find all missing dimensions on the triangles in the image.  This includes all missing sides and angles in each right triangle.  This is also known as "Solving the Triangles".

AUDIENCE:  The poor skateboarders that keep falling on the destroyed ramp and the construction crew that is going to do the actual rebuilding.  The crew is waiting on the plans.

SITUATION:  Use the skills you have learned about the Pythagorean theorem, special right triangles, and trigonometric ratios to find every missing side and every missing angle in each triangle in the image.

PERFORMANCE:  Accurately calculate, to the nearest tenth, the missing sides and three missing angles in each of the triangles.  Show all of your work and calculations for each missing side or angle.  Explain in complete sentences all of your steps and display the answers in the correct units.  
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1 Answer

AB = √(5^2 + 10^2) = √(5^2 + (2*5)^2)
= √(5^2 (1 + 2^2)) = 5√(5) ≈ 11.18033988749895 ≈ 11.2 ft
∠ABD = arctan(1/2) ≈ 26.56505117707799 ≈ 26.6°
∠BAD ≈ 90° - 26.6° ≈ 63.4°
 
10/BC = sin(30°), this is special Δ 30°-60°-90° w/sides 1:√(3):2
BC = 10/sin(30°) = 10/(1/2) = 20 ft
DC = 10*√(3) ≈ 17.32050807568877 ≈ 17.3 ft
∠CBD = 60°