The diagram below shows part of a climbing frame - Junior Cycle Mathematics - Question 8 - 2017
Question 8
The diagram below shows part of a climbing frame. The points B and C are on the ground. She finds that they are both 55°.
(a) What type of triangle is ABC? Give a r... show full transcript
Worked Solution & Example Answer:The diagram below shows part of a climbing frame - Junior Cycle Mathematics - Question 8 - 2017
Step 1
What type of triangle is OBC? Give a reason for your answer.
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Answer
The triangle OBC is an Isosceles triangle because it has two equal angles of 55°.
Reason: Two of the angles are the same.
Step 2
Work out the size of the angle at O, the top of the frame.
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Answer
To find the angle at O, we can use the fact that the sum of angles in a triangle is 180°.
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Answer
The triangles OBC and OPS are similar, which means they have the same shape, but their sizes may differ. This is because they share corresponding angles that are equal: OBC has base angles of 55° and tops angles that reflect this structure, indicating that their sides are proportional.
Step 4
Find the length |BC|.
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Answer
To find the length |BC|, we use the properties of similar triangles that state that the ratios of corresponding sides are equal.
