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The diagram below shows the angle A in a right-angled triangle - Junior Cycle Mathematics - Question 12 - 2012
Question 12
The diagram below shows the angle A in a right-angled triangle. Indicate which side is adjacent and which is opposite in relation to the angle A, and which side is t... show full transcript
Worked Solution & Example Answer:The diagram below shows the angle A in a right-angled triangle - Junior Cycle Mathematics - Question 12 - 2012
Step 1
Indicate which side is adjacent, opposite, and hypotenuse.
Answer
In the right-angled triangle:
- The side opposite angle A is referred to as the 'Opposite Side.'
- The side adjacent to angle A is referred to as the 'Adjacent Side.'
- The longest side, which is opposite the right angle, is known as the 'Hypotenuse.'
Step 2
Step 3
Find the length of the hypotenuse correct to the nearest centimetre.
Answer
To find the hypotenuse, we use the sine ratio:
ext{Sin } 35° = rac{ ext{Opposite}}{ ext{Hypotenuse}}Substituting the values gives:
0.5736 = rac{12}{x}Rearranging to solve for x (the hypotenuse):
x = rac{12}{0.5736} \ x ≈ 20.9205 ext{ cm}Rounding to the nearest centimetre, the length of the hypotenuse is approximately 21 cm.