Question

Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.

Answer 1

Explanation:

Lets name the perpendicular drawn from vertex to opposite side " h " for calculation purposes (Refer the figure attached)

so first in the triangle ABC,

`tan(30) = (BC)/(AC)`

`tan(30) = (16)/(h)`

`h= (16)/(tan(30))`

`h =16√(3)`

Now refer the triangle ACD , there we can use the trigonometric ratio

`cos(41) =(AC)/(AD)`

`cos(41) =(16√(3) )/(x)`

`x =(16√(3) )/(cos(41))`

x= 36.7