Higher June 2018 Paper 3 Q5
5 \(ABC\) is a right-angled triangle.
(a) Work out the size of angle \(ABC\).
Give your answer correct to 1 decimal place. (2)
Give your answer correct to 1 decimal place. (2)
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 \(90^\circ\)
(b) Will the value of \(\cos ABC\) increase or decrease?
You must give a reason for your answer. (1)
You must give a reason for your answer. (1)
| Answer | Mark | Mark scheme |
|---|---|---|
| 50.5 | M1 | for \(\cos ABC = \dfrac{7}{11}\) (0.63…) oe |
| A1 | for answer in the range 50.4 to 50.51 |
Additional guidance
Must be a complete statement for cos, sin or tan with all three elements present.
If an answer is in the range 50.4 to 50.51 is given in the working space then incorrectly rounded, award full marks.
| Answer | Mark | Mark scheme |
|---|---|---|
| Increase (supported) | C1 | States increase with supporting reason eg “\(\dfrac{7}{10}\) is greater than \(\dfrac{7}{11}\)” “0.636 is less than 0.7” ….“cos increases as angle decreases” “decreasing the denominator increases the value of the fraction” “angle is now 45.6” (accept 45.5 – 45.6) |
Additional guidance
If figures are given they must be correct (truncated or rounded).