Question

Special right triangles

Answer 1

Answer:

x=14.4

Step-by-step explanation:

We apply the Sine Rule to solve for x:

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

$\frac{a}{Sin \ A}=\frac{b}{Sin \ B}=\frac{c}{Sin \ C}\\\\\frac{30}{Sin \ 90\textdegree}=\frac{24}{Sin \ A\textdegree}\\\\A=53.13\textdegree$

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

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

$\frac{x}{Sin \ 53.13\textdegree}=\frac{18}{Sin \ 90\textdegree}\\\\x=14.4$

Hence, the length of x is 14.4