Question

Special right triangles

Answer 1

x=14.4

Explanation:

We apply the Sine Rule to solve for x:

#We first determine the acute angles of the larger right angles.

`(a)/(Sin \ A)=(b)/(Sin \ B)=(c)/(Sin \ C)\\\\(30)/(Sin \ 90\textdegree)=(24)/(Sin \ A\textdegree)\\\\A=53.13\textdegree`

The smaller right angles shares one acute angle of 53.13°.

Therefore the x can be solved applying the Sine Rule again:

`(x)/(Sin \ 53.13\textdegree)=(18)/(Sin \ 90\textdegree)\\\\x=14.4`

Hence, the length of x is 14.4