Unit 4
4 marks · EasyA straight road runs from point A to B, 500 m away. A tree is planted at point C, which is exactly 300 m from A along the road.
Write down the length of AC.
Calculate the distance from B to C.
If a right-angled triangle is formed at C with the other vertex D, such that DC = 400 m and angle CAD = 90°, use Pythagoras’ theorem to calculate the length of DA.
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
(a) 300 m
(b) 200 m
(c) 500 m
Common mistakes: Confusing sides of triangle; Using Pythagoras incorrectly
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · States AC = 300 m
B2 (b) · 1 mark · BC = 500 - 300 = 200 m
M1 (c) · 1 mark · Identifies use of Pythagoras' theorem
A1 (c) · 1 mark · Finds DA = 500 m using calculation DA^2 = 400^2 + 300^2
Worked solution
a) Length AC = 300 m.
b) BC = AB - AC = 500 - 300 = 200 m.
c) Using Pythagoras: DA^2 = DC^2 + CA^2 = 400^2 + 300^2 = 160000 + 90000 = 250000, so DA = √250000 = 500 m.