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Skate and Climb: Diagonal Checks

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Skate and Climb: Diagonal Checks

Use right triangles to check ramps, routes, and equipment clearances.

Ramps and Wall Routes

Use the Pythagorean Theorem. All measurements describe straight segments. Give exact answers unless rounding is requested.

1.
A skate ramp has a horizontal run of 12 ft and a vertical rise of 9 ft. These form the legs of a right triangle.

What is the length of the sloping surface? ft

2.
A straight climbing-wall route is 13 m long. Its finish is 5 m horizontally from its start. The horizontal and vertical changes are perpendicular.

How much higher is the finish than the start? m

3.
This coordinate grid shows a triangular panel on the climbing wall. Each coordinate unit represents 1 ft. Segment AC is the diagonal route.−8−6−4−224680−8−6−4−22468ABC

What is the length of AC? ft

4.
A triangular ramp support has perpendicular legs of 5 ft and 7 ft. Which expression gives the exact length of its diagonal brace?
Question 4 options
5.
A practice ramp rises 1.5 m over a horizontal run of 2 m. The floor is level.

How long is the sloping surface? m

Membership Route Checks

Use a right-triangle model to make each decision. Ignore material thickness and stretching.

6.
Members can cross a rectangular practice zone by following two adjoining edges or by taking a straight diagonal route. The zone is 8 m wide and 15 m long.

How much shorter is the diagonal route than following the two edges? m

7.
A rectangular landing mat is 10 ft wide and 24 ft long. A strap must span its diagonal in a straight line, with at least 1 ft left over for fastening. Which listed strap is the shortest one that works?
Question 7 options
8.
An advanced-membership route uses a taut, straight training cable. The cable is 17 m long, and its upper anchor is 15 m directly above the level floor. Its lower anchor is on the floor.

What is the horizontal distance from the lower anchor to the point directly below the upper anchor? m

9.
The gym's rectangular training room is 6 m wide, 7 m long, and 6 m high. A straight cable runs from one floor corner to the opposite ceiling corner.

How long is the cable? m

Inside Three-Dimensional Spaces

Use a face diagonal when needed, then form another right triangle. A rectangular prism has three mutually perpendicular edge directions.

10.
The gym stores route-marking rods in a rectangular cabinet with inside dimensions of 2 ft, 3 ft, and 6 ft. A straight rod can fit along the cabinet's space diagonal, and touching the cabinet's interior corners is allowed. Which listed rod is the longest that fits?
Question 10 options
11.
A rectangular climbing frame has a 12 ft by 16 ft base. A brace from one bottom corner to the opposite top corner is 25 ft long.

What is the frame's height? ft

12.
A rectangular equipment enclosure measures 4 m wide, 6 m long, and 9 m high. What is the distance from one bottom corner to the opposite top corner, rounded to the nearest tenth?
Question 12 options
13.
A rectangular gym room is 12 m long, 9 m wide, and 8 m high. Nia finds the floor diagonal: √(12² + 9²) = 15 m. She then treats the cable as a leg and says it must be √(15² − 8²) = √161 ≈ 12.7 m long. Explain her mistake and find the correct cable length.