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Bridge Design Geometry Challenge

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Bridge Design Geometry Challenge

A council is planning a small footbridge over a creek. Use geometry to check a scale design before it is built. All measurements are in metres unless stated otherwise. Show working for calculations and include units.

Check the frame

The bridge side frame is made from repeating triangles. Use the measurements in each question.

1.One right-triangle brace has horizontal and vertical legs of 3 m and 4 m. Find its length. Give your answer to the nearest tenth of a metre.

2.A second brace makes an angle of 35° with the horizontal deck. What is the other acute angle in its right-triangle frame? Explain briefly.

3.The deck is 18 m long. It is divided into six equal bays for the truss panels. What is the length of each bay?

4.A rectangular viewing platform is 4.5 m long and 2 m wide. Calculate its area.

Scale, similarity and angles

The engineer checks whether the design is consistent from one end of the bridge to the other.

5.A small model truss has sides 6 cm, 8 cm and 10 cm. A full-size similar truss has its shortest side measuring 1.5 m. Find the scale factor from model to full size, then give the other two full-size side lengths.

6.Each side panel is an isosceles triangle with two equal 5 m braces and a 6 m base. Find the perpendicular height from the top vertex to the base. Hint: the height bisects the base.

7.A triangular panel has angles 35° and 65°. Calculate the third angle, then classify the triangle by its angles.

8.Which condition is sufficient to prove that two triangular panels are congruent?

Their areas are equal.
Their corresponding three side lengths are equal.
They have one equal angle.
They are both triangles.

Make a geometric design decision

Use the design facts below to evaluate a proposed change.

Panel 1: 3 m × 4 m right triangle; diagonal brace = ?

Panel 2: same dimensions as Panel 1; diagonal brace = ?

Panel 3: same dimensions as Panel 1; diagonal brace = ?

9.Use the panel plan: calculate the diagonal length for one panel and the total diagonal-brace length for all three panels.

10.A designer suggests replacing each triangular panel with a rectangular panel that has no diagonal brace. Explain, using a geometric property, why the original triangles are a more rigid frame.

11.A bridge engineer checks a scale sketch where 1 cm represents 2 m. The deck measures 9 cm on the sketch. What is its real length?