In ΔXYZ, ∠Y=90° and ∠X=16°. ∠ZWY=42° and XW=260. Find the length of ZY to the nearest integer. (9th grade honors geometry)

Step-by-step explanation:

[tex] \tan(16) = \frac{y}{260 + x} \\ (260 + x) \times \tan(16) = y \\ 74.55 + 0.286x = y \\ y = 0.286x + 74.55[/tex]

[tex] \tan(42) = \frac{y}{x} \\0.9 x = y[/tex]

[tex]0.9x = 0.286x + 74.55 \\ 0.614x = 74.55 \\ x = 121.42[/tex]

[tex]y = 0.9x \\ y = 109.27 = 109[/tex]

The length of ZY is [tex]109.27[/tex]

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.

What is length?

Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the International System of Units system the base unit for length is the meter.

According to question, In ΔXYZ, ∠Y=90° and ∠X=16°. ∠ZWY=42° and XW=260.

We have to find the  the length of ZY.

Let the length of ZY be [tex]x[/tex] and WY be [tex]y[/tex]

From the given question and figure

[tex]tan16[/tex]°[tex]=\frac{y}{260+x}[/tex]

⇒[tex]tan16[/tex]°×[tex](260+x)=y[/tex]

⇒[tex]y=0.286x+74.55[/tex]

Now,[tex]tan42[/tex]°[tex]=\frac{y}{x}[/tex]

⇒[tex]y=0.9x[/tex]

From both the above equation,

[tex]0.9x=0.286x+74.55[/tex]

⇒[tex]x=121.42[/tex]

[tex]y=0.9x=109.27[/tex]

Hence, we can conclude that the length of ZY is [tex]109.27[/tex]

Learn more about  trigonometry here:

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