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 length of the side BC is still 7 cm. Angle ACB is still 90°. (b) Will the value of cos ABC increase or decrease? You must give a reason for your answer.

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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.

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Answer

To find angle ABC in triangle ABC, we can use the cosine function, defined as:

$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

In this case:

The adjacent side (BC) = 7 cm
The hypotenuse (AB) = 11 cm

Thus, we can calculate:

$\cos(ABC) = \frac{7}{11}$

Using a calculator to determine the angle, we have:

$ABC = \cos^{-1}\left(\frac{7}{11}\right)$

Calculating this yields:

$ABC \approx 49.5°$

Rounding to 1 decimal place gives: 49.5°.

Step 2

Will the value of cos ABC increase or decrease?

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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 $\frac{\text{adjacent}}{\text{hypotenuse}}$ increases.

Hence, the value of cosine increases because decreasing the denominator increases the value of the fraction.

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