Shape and Space 4
4 marks · NormalThe diagram shows a right-angled triangle XYZ where Y is the right angle, XY = 7.8 cm and angle ZXY = 38°.
(a) Calculate the length XZ.
(b) Find the length YZ. Give your answer to 2 decimal places.
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(a) 10.0 cm
(b) 6.30 cm
Common mistakes: Using incorrect ratio; Mixing up given side and side to find
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Recognises side XY is adjacent and XZ is hypotenuse for angle at X, sets up
A1 (a) · 1 mark · Finds XZ = 10.0 cm (2 or 3 significant figures allowed) (follow-through)
M1 (b) · 1 mark · Sets up equation for YZ (opposite for angle 38°, uses sine or Pythagoras with just determined hypotenuse). (follow-through)
A1 (b) · 1 mark · Finds YZ = 6.30 cm (2 d.p.) (follow-through)
Worked solution
Let x = XZ.
Now, to find YZ (opposite side to 38°),