MathsFreePrintable

Angles in Sports Scenarios

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Download now

Name:Date:

Angles in Sports Scenarios

At a dance competition, Cooper, Tahnee and Kirra are planning floor patterns. Use angle facts and trigonometry to solve each challenge. Give units where needed and round lengths to 1 decimal place and angles to the nearest degree unless stated otherwise.

Read the floor

Assume the straight floor markings shown are ideal lines. Diagrams are not necessarily drawn to scale.

1.Tahnee turns from one direction to the opposite direction along a straight floor marking. One of the adjacent angles is 128°. Find the other angle, x, and state the angle fact you used.

2.Cooper and Kirra's floor pathways cross. The angle between two adjacent pathways is 67°. What is the vertically opposite angle? Explain why.

3.Match each dance-floor situation to the angle relationship that applies. Situation A: two angles share a vertex and one arm, with the other arms forming a straight line. Situation B: a pair of angles lie opposite each other where two straight pathways cross. Situation C: two angles add to 90°.

Vertically opposite angles
Complementary angles
Linear pair (supplementary)

4.Kirra's choreography makes a right angle between two steps. One step is 34° from the stage's front edge. Find the angle between the other step and the front edge.

34°
56°
90°
146°

Use triangles and trigonometry

For the next challenges, sketch or use the supplied angle information to choose a suitable geometric relationship. Show your working.

5.The three angles inside a triangular floor formation are 48°, 71° and x°. Find x.

6.A rectangular stage is 12 m long and 5 m wide. Cooper crosses diagonally from one corner to the opposite corner. What angle does the diagonal make with the 12 m side? Give your answer to the nearest degree.

7.A spotlight is 8 m horizontally from a point on the floor directly beneath a raised lighting platform. The platform is 6 m above the floor. Find the angle of elevation from the spotlight to the platform, to the nearest degree.

8.Tahnee and Kirra stand at two points 10 m apart. Cooper stands 7 m from Tahnee and 9 m from Kirra. Find the angle at Cooper, opposite the 10 m side. Round to the nearest degree.

9.A choreographer says that if one angle in a triangle is 90° and another is 38°, the third angle must be 62°. Is the claim true or false? Correct it if needed.

TrueFalse

10.Cooper's pathway makes an angle of 32° with the front edge of the stage. A second pathway must be perpendicular to Cooper's pathway. What acute angle will the second pathway make with the front edge? Explain briefly.