Question

Calculate the length w in the shape below.
Give your answer in centimetres to 2 d.p.

Answer 1

w = 12.14 cm

Explanation:

See the attached image. Trigonometric functions will be used

Answer 2

w ≈ 12.14 cm

Explanation:

using the tangent ratio in the right triangle on the left.

let vertical height be x

tan56° =
`(opposite)/(adjacent)` =
`(x)/(3.2)` ( multiply both sides by 3.2 )

3.2 × tan56° = x , then

x ≈ 4.744

using the cosine ratio in the right triangle on the right

cos67° =
`(adjacent)/(hypotenuse)` =
`(x)/(w)` =
`(4.744)/(w)` ( multiply both sides by w )

w × cos67° = 4.744 ( divide both sides by cos67° )

w =
`(4.744)/(cos67)` ≈ 12.14 cm (to 2 decimal places )