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Construct a right-angled triangle ABC, where: |AB| = 6 cm |∠ABC| = 90° |AC| = 10 cm - Junior Cycle Mathematics - Question i - 2014

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Construct a right-angled triangle ABC, where: |AB| = 6 cm |∠ABC| = 90° |AC| = 10 cm. (ii) On your diagram, measure the angle ∠CAB. Give your answer correct to th... show full transcript

Worked Solution & Example Answer:Construct a right-angled triangle ABC, where: |AB| = 6 cm |∠ABC| = 90° |AC| = 10 cm - Junior Cycle Mathematics - Question i - 2014

Step 1

Construct a right-angled triangle ABC

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Answer

  1. Begin by placing point A on your drawing.
  2. From point A, draw a horizontal line segment of length 6 cm towards point B.
  3. Construct point C such that |∠ABC| = 90° and |AC| = 10 cm. To find point C, use the Pythagorean theorem: ∣BC∣=∣AC∣2−∣AB∣2=102−62=100−36=64=8cm.|BC| = \sqrt{|AC|^2 - |AB|^2} = \sqrt{10^2 - 6^2} = \sqrt{100 - 36} = \sqrt{64} = 8 cm.
  4. Connect points A and C, and then connect points B and C, forming triangle ABC.

Step 2

Measure the angle ∠CAB

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Answer

Using a protractor, place the center hole of the protractor at point A and align one side of the angle with line segment AC. Read the angle measurement at line segment AB. Based on the measurement, the angle |∠CAB| = 53° (rounded to the nearest degree).

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