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GeoGebra Pythagoras Exploration

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GeoGebra Pythagoras Exploration

Aotearoa’s volunteer search-and-rescue team is planning routes and equipment for a mountain hut. Use Pythagoras’ theorem to calculate right-triangle lengths in 2D and 3D. Show working and round answers to 2 decimal places where needed. You do not need GeoGebra to complete this worksheet.

Right-triangle investigations

1.A rescue team maps a straight path across a rectangular field. The path is the hypotenuse of a right triangle with legs 9 m and 12 m. Find its length, then verify your result using a² + b² = c².

2.A trail rises 18 m vertically while moving 24 m horizontally. Which calculation gives the straight-line distance up the trail?

√(18 + 24) = 6.48 m
√(18² + 24²) = 30 m
18 + 24 = 42 m
24² − 18² = 252 m

3.A surveyor measures the two shorter sides of a right triangle as 7.5 m and 10 m. Calculate the hypotenuse to 2 decimal places.

4.A cable is 13 m long and is attached from the top of a pole to a ground anchor 5 m from the pole’s base. How high up the pole is it attached?

Three-dimensional Pythagoras

5.A rectangular equipment crate measures 3 m × 4 m × 12 m. Calculate the length of a space diagonal from one corner to the opposite corner.

6.Select the correct space-diagonal formula for a cuboid with edge lengths a, b and c.

d = a + b + c
d² = a² + b²
d² = a² + b² + c²
d = abc

7.A rectangular hut is 8 m long, 6 m wide and 3 m high. A cable runs from a bottom corner to the opposite top corner. Find the cable length to 2 decimal places.

8.A drone flies from one corner of a level rectangular landing area, 40 m by 30 m, to the opposite corner, then climbs vertically 24 m. What is its straight-line distance from its starting point?

Check and explain

9.Mere calculates the diagonal of a 3 m × 4 m × 5 m crate as √(3² + 4²) = 5 m. Explain what she has found and how to calculate the crate’s space diagonal.

10.A team needs to order a support cable for a 45 m tower. The ground anchor is 20 m from the base. They add 2 m for connections. How much cable should they order, to the nearest whole metre?