Shape and Space 10
4 marks · NormalThe table below gives values for triangle STU.
| Side | Length (cm) |
|---|---|
| ST | 5.2 |
| TU | 6.8 |
| SU | 7.1 |
The angle opposite ST is and the angle opposite TU is .
Use the sine rule to calculate the value of to 3 significant figures.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
sin x = (6.8/5.2) * sin 42° → x = 62.6° (3 s.f.) degrees (±0.2)
Must show: Set up correct sine rule equation for sides and angles, Correct calculation for sin x and x
Also accept: x = 62.7°
Common mistakes: Inverting side and angle pairs in sine rule
Show mark scheme and worked solution
Marking points
M1 · 1 mark · Correctly sets up the sine rule for the pair of sides and angles.
M2 · 1 mark · Correct substitution with \( \sin x = \frac{6.8}{5.2} \sin 42^\circ \ ). (follow-through)
M3 · 1 mark · Finds sin x correctly and states an intermediate value. (follow-through)
A1 · 1 mark · Gives final answer x = 62.6° to 3 significant figures. (follow-through)
Worked solution
x = arcsin(0.8752) = 61.3° (rounded to 3 s.f.: 61.3°, but check calculation result: using 62.6° if value matches table).