Shape and Space 3
4 marks · HardA ladder leans against a vertical wall and reaches a point 7.2 m above the ground. The foot of the ladder is 2.7 m from the base of the wall.
Calculate the angle, to the nearest degree, that the ladder makes with the ground.
Find the angle described and show your full working.
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
69° degrees (±1)
(a) 69° degrees
Also accept: 68°; 69°; 70°
Common mistakes: Using sine or cosine instead of tangent; Incorrect ratio setup
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Correct ratio for set up.
M2 (a) · 1 mark · Attempts to calculate the inverse tangent (arctan) of the ratio. (follow-through)
A1 (a) · 1 mark · Obtains . (follow-through)
A2 (a) · 1 mark · Rounds correctly to the nearest degree (69°). (follow-through)
Worked solution
Let be the angle the ladder makes with the ground. In the right-angled triangle formed, the vertical height (opposite) is 7.2 m and the base (adjacent) is 2.7 m.
To the nearest degree, .