Question

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

Answer 1

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

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.

`(Sin A)/(a) = (SinB)/(b) = (SinC)/(c)`

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

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

Then,

`(Sin80)/(17) = (SinZ)/(14)`

Using cross multiplication:-

⇒
`SinZ * 17 = Sin80 * 14`

⇒
`SinZ=(Sin80*14)/(17)`

⇒
`SinZ= 0.8110`

⇒ ∠
`Z=Sin^(-1)(0.8110)`

⇒ ∠
`Z=54.2`°

Hence,

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