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ABC is a right-angled triangle - Edexcel - GCSE Maths - Question 6 - 2018 - Paper 3
Question 6
ABC is a right-angled triangle. (a) Work out the size of angle ABC. Give your answer correct to 1 decimal place. The length of the side AB is reduced by 1 cm. The ... show full transcript
Worked Solution & Example Answer:ABC is a right-angled triangle - Edexcel - GCSE Maths - Question 6 - 2018 - Paper 3
Step 1
Work out the size of angle ABC.
Answer
To find angle ABC in triangle ABC, we can use the cosine function, defined as:
In this case:
- The adjacent side (BC) = 7 cm
- The hypotenuse (AB) = 11 cm
Thus, we can calculate:
Using a calculator to determine the angle, we have:
Calculating this yields:
Rounding to 1 decimal place gives: 49.5°.
Step 2
Will the value of cos ABC increase or decrease?
Answer
The value of cos ABC will increase when the side AB is reduced by 1 cm.
When AB decreases:
- The hypotenuse becomes less than before. This means the adjacent side (BC) remains constant at 7 cm, while the hypotenuse now is less than 11 cm.
- Consequently, the ratio increases.
Hence, the value of cosine increases because decreasing the denominator increases the value of the fraction.