Question

Given that y= 8 cm and θ= 39 °, work out x rounded to 1 decimal place.

(not drawn to scale)

Answer 1

x ≈ 6.2 cm

Explanation:

using the cosine ratio in the right triangle

cosΘ =
`(adjacent)/(hypotenuse)` , that is

cos39° =
`(x)/(y)` =
`(x)/(8)` ( multiply both sides by 8 )

8 × cos39° = x , then

x ≈ 6.2 cm ( to 1 dec. place )

Answer 2

x = 6.2

Use cosine rule:

`\sf cos(\theta) = (adjacent)/(hypotenuse)`

Inert following:

`\sf cos(39) = (x)/(8)`

change sides

`\sf x = 8cos(39)`

simplify

`\sf x = 6.2`