Question

in angle XYZ, m/_ y=80, XY= 14, and XZ=17. to the nearest tenth, what is m/_ z​

Answer 1

Answer:

Using Sine rule we found the measure of ∠$Z=54.2$°.    

Step-by-step explanation:

Diagram of the given condition shown below.

Given that,

In Triangle Δ$XYZ$,

       ∠$Y = 80$°  ,  $XY = 14, & \ XZ=17$.

To find :- What is the measure of ∠$Z$.

So,

Using Sine rule :-  sine rule relates the sine of each angle to length of        opposite side.

                     $\frac{Sin A}{a} = \frac{SinB}{b} = \frac{SinC}{c}$

                                                Where,  $A,B,C$  are angles of triangle Δ$ABC.$

                                                                   $a,b,c$  are side length of triangle.

Then,      

                            $\frac{Sin80}{17} = \frac{SinZ}{14}$

Using cross multiplication:-

  ⇒            $SinZ \times 17 = Sin80 \times 14$

  ⇒                $SinZ=\frac{Sin80\times14}{17}$

  ⇒                 $SinZ= 0.8110$

  ⇒                      ∠$Z=Sin^{-1}(0.8110)$

  ⇒                     ∠$Z=54.2$°

Hence,

Using Sine rule we found the measure of ∠$Z=54.2$°.