Higher November 2022 Unit 2 Q14
14. \(DE\) is the tangent to the circle at point \(A\), as shown below.
\(BC\) = 7 cm and \(AC\) = 13 cm.
\(B\hat{A}D = 68^\circ\) and \(C\hat{A}E = 80^\circ\).
Diagram not drawn to scale
(a) Find the size of \(A\hat{C}B\).
State the angle property you have used to find your answer. [2]
State the angle property you have used to find your answer. [2]
(b) Calculate the area of the triangle \(ABC\). [2]
From the formula list: In any triangle \(ABC\): Area of triangle \(= \dfrac{1}{2}ab\sin C\)
| Scheme | Marks | Comments |
|---|---|---|
| 68(°) AND alternate segment theorem. | B2 | Do not accept ‘alternate (angle) theorem’ or ‘alternate angles’ only as the given angle property. 68(°) may be seen on the diagram at ACB. B1 for 68(°) Award B0 for any angle other than ACB clearly identified as 68(°) |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| Allow a correct and complete method that results in an angle of 68(·219…°) AND relevant angle property (e.g. angles on a straight line OR angles in a triangle OR using the sine rule). | B2 | Allow B1 for a correct and complete method that results in an angle of 68(·219…°). |
| Scheme | Marks | Comments |
|---|---|---|
| \(1/2 \times 7 \times 13 \times \sin 68(^\circ)\) | M1 | FT ‘their 68’ identified as their ACB from part (a). Award M1 for a complete alternative method leading to a correct answer of 42·1(… cm2) OR 42·2(cm2). |
| = 42·1(86… cm2) OR 42·2(cm2) | A1 |