Question

Find the missing side. Round
to the nearest tenth.
Х
у
39
57
y = [?]

Answer 1

Y = 46.2. View the picture to see steps

Answer 2

In the given triangle value of $x= 73.4$ units and $y= 46.2$ 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

$tan\theta = \frac{perpendicular side}{adjacent side}$

According to the question,

In the given triangle,

Hypotenuse $= x$

Perpendicular side $= y$

Adjacent side $= 57$

Value of $\theta = 39$

Substitute the value of the given triangle in the formula to get the missing values,

$tan 39\°= \frac{y}{57} \\\\\implies 0.8098 = \frac{y}{57}\\\\\implies y = 57 \times 0.8098\\\\\implies y = 46.1586$

$\implies y= 46.2$ units (round to nearest tenth)

Substitute the value in the Pythagoras theorem we get,

$x^{2} = (46.2)^{2} +(57)^{2} \\\\\implies x^{2} = 2134.44 + 3249\\\\\implies x = \sqrt{5383.44} \\\\\implies x = 73.37$

$\implies x = 73.4$ units (round to nearest tenth)

Hence, In the given triangle value of $x= 73.4$ units and $y= 46.2$ units ( round to nearest tenth)

Learn more about triangle here

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