In the given triangle value of [tex]x= 73.4[/tex] units and [tex]y= 46.2[/tex] units ( round to nearest tenth)
What is triangle?
" Triangle is defined as the two dimensional geometrical shape with three vertices, three sides and three angles enclosed in it."
Formula used
Pythagoras theorem
(Hypotenuse)² = (adjacent side)² + (perpendicular side)²
[tex]tan\theta = \frac{perpendicular side}{adjacent side}[/tex]
According to the question,
In the given triangle,
Hypotenuse [tex]= x[/tex]
Perpendicular side [tex]= y[/tex]
Adjacent side [tex]= 57[/tex]
Value of [tex]\theta = 39[/tex]
Substitute the value of the given triangle in the formula to get the missing values,
[tex]tan 39\°= \frac{y}{57} \\\\\implies 0.8098 = \frac{y}{57}\\\\\implies y = 57 \times 0.8098\\\\\implies y = 46.1586[/tex]
[tex]\implies y= 46.2[/tex] units (round to nearest tenth)
Substitute the value in the Pythagoras theorem we get,
[tex]x^{2} = (46.2)^{2} +(57)^{2} \\\\\implies x^{2} = 2134.44 + 3249\\\\\implies x = \sqrt{5383.44} \\\\\implies x = 73.37[/tex]
[tex]\implies x = 73.4[/tex] units (round to nearest tenth)
Hence, In the given triangle value of [tex]x= 73.4[/tex] units and [tex]y= 46.2[/tex] units ( round to nearest tenth)
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