Question

Find the value of the length x rounded to 1 DP.

Answer 1

x = 13.6 (1 dp)

Explanation:

Using the following trig ratio to calculate the base of each triangle:

`tan(\theta)=(O)/(A)`

where
`\theta` is the angle, O is the side opposite the angle and A is the side adjacent to the angle.

Left triangle

Given:

• 
  `\theta` = 39
• O = 6
• A =
  `x_1`

`\implies tan(39) = (6)/(x_1)`

`\implies x_1 = (6)/(tan(39))`

Right triangle

Given:

• 
  `\theta` = 44
• O = 6
• A =
  `x_2`

`\implies tan(44) = (6)/(x_2)`

`\implies x_2 = (6)/(tan(44))`

Length of x

`x = x_1+x_2`

`\implies x=(6)/(tan(39))+(6)/(tan(44))`

`\implies x=13.6` (1 dp)

Answer 2

x = 13.6 cm

Explanation:

part A:

using tan rule:

`tan(x) = (opposite)/(adjacent)`

`tan(39) = (6)/(adjacent)`

`adjacent = (6)/(tan(39))`

`adjacent = 7.41`

part B:

using tan rule:


`tan(x) = (opposite)/(adjacent)`

`tan(44) = (6)/(adjacent)`

`adjacent = 6.213`

Total length of x:

part A + part B

`7.41 + 6.213`

`13.6` cm