Use familiar mathematics to make and test decisions.

You will compare two panels, design cable anchors and choose a camera position. No new HL content is required. Your task is to decide how to combine the methods you already know.

Work with a partner, but keep your own labelled diagrams, calculations and explanations. Use your GDC in degree mode. Keep full precision until the final answer.

Use the final 19 minutes for the independent check and corrections. Open a hint only after an attempt; open the worked answer after recording your reasoning.

Two triangular panels each have sides of 8 cm and 13 cm. The included angle is 53° in panel A and 127° in panel B.

Predict which panel has greater area and which needs more edging. Then calculate the area and perimeter of each.

A manufacturer requires an area of at least 40 cm² and a perimeter no greater than 34 cm. Decide which panel meets both conditions.

Explain how equal area can occur even though the panels are not congruent.

Keep the two sides at 8 cm and 13 cm, but choose new included angles.

Create a pair of different triangles with equal areas larger than 41.5 cm². Then create a second pair with equal areas smaller than 41.5 cm².

For every triangle, give its included angle and verify the area. Compare with another pair: how many different answers could be valid?

Find the greatest possible area with these two sides. Explain geometrically why no design can exceed it.

A straight cable is exactly 13 m long. It starts at A = (0, 0, 1). The third coordinate is height above level ground.

The anchor B must lie on the wall x = 3, with 0 ≤ y ≤ 10 and z > 1. The cable must make an angle no greater than 60° above the ground.

A designer proposes B = (3, 4, 13). Does this use the full cable? Does it satisfy the angle restriction?

Show the planar distance and vertical rise. Passing one requirement does not guarantee that the design is acceptable.

Keep A = (0,0,1), the 13 m cable and the wall x = 3. The anchor still requires 0 ≤ y ≤ 10, z > 1 and an elevation at most 60°.

Create two acceptable anchors with different heights. Verify every restriction.

Choose a vertical rise first, then calculate the required y-coordinate. Or choose y first and work backwards to the height. State coordinates exactly where practical.

The same conditions apply: A = (0,0,1), cable length 13 m, wall x = 3, 0 ≤ y ≤ 10, z > 1 and elevation at most 60°.

Find the smallest possible y-coordinate and the greatest possible anchor height. Then describe every acceptable anchor using y.

Explain which condition controls each boundary. Check whether the boundary values themselves are allowed.

B is 600 m due east of A. A drone is vertically above ground point C. The bearing of C from A is 040°; the bearing from B is 310°. The drone is 150 m above C.

Find AC and BC. Then locate C using coordinates with A = (0,0), east as positive x and north as positive y.

M is the midpoint of AB. Calculate MC without measuring the drawing. Keep unrounded values for the next slide.

The drone is 150 m above C. From the survey, AC ≈ 385.7 m and MC = 300 m, where M is the midpoint of AB.

A camera may be placed at A or M. Its straight-line range is at most 400 m, and its viewing angle above the ground must be between 20° and 30° inclusive.

Test both positions against both conditions. Recommend a location with numerical evidence.

At your chosen location, find the full range of drone heights that still satisfies both camera limits.

Review the independent check. Choose one step to correct or one answer to justify more fully.

Which condition controlled the decision? How did you check that every other condition was also satisfied?

Write a short explanation identifying the diagram, mathematical method and final interpretation. A correct length does not settle an angle restriction; a sufficient area does not settle a perimeter restriction.

Finish by writing one connection that helped you solve a less familiar problem using mathematics you already knew.