Question

In the right triangle shown in the diagram below, what is the value of x to the nearest whole number?

Answer 1

`x=21`

Explanation:

See attachment for triangle

The relationship between length x, length 24 and angle 30 is as follows:

`\cos(\theta) = (Adjacent)/(Hypotenuse)`

In this question;

`Adjacent = x`

`Hypotenuse= 24`

`\theta = 30`

Substitute these values in the above expression,

`\cos(30) = (x)/(24)`

Multiply through by 24

`24 * \cos(30) = (x)/(24) * 24`

`24 * \cos(30) = x`

Reorder:

`x = 24 * \cos(30)`

`x = 24 * 0.8660`

`x = 20.784`

`x=21` --- approximated