Shape and Space 4

3 marks · Normal

A ladder 4.5 m long leans against a vertical wall, making an angle of 68° with the ground. Calculate the height above the ground that the top of the ladder reaches.

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

4.17 m (±0.02)

Also accept: 4.2

Common mistakes: using cosine instead of sine; calculating the base instead of the height

Show mark scheme and worked solution

Marking points

M1 · 1 mark · Identifies and writes the correct trigonometric ratio:

M2 · 1 mark · Correctly rearranges and substitutes values: (follow-through)

A1 · 1 mark · Final answer correct to 3 s.f. (follow-through)

Worked solution

Let h be the vertical height the top of the ladder reaches. In the right triangle, the ladder is the hypotenuse and the height is opposite the 68° angle at the base.

So the height is 4.17 m (to 3 s.f.).