Mathematics
02.09.2022 10:46
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QUESTION 1 Find the remaining sides of a 30° -60°-90° triangle if the shortest side

QUESTION 1
Find the remaining sides of a 30° -60°-90° triangle if the shortest side is 3.
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MelissaSmartypants
MelissaSmartypants
4,4(29 marks)

x = 6

Step-by-step explanation:

Right Triangle

We are given a right triangle whose shortest side has a length of 3 units. This side must be opposite to the smallest acute angle of 30°.

The triangle is shown in the figure attached.

The tangent ratio relates the opposite side with the adjacent side. The formula can be applied to the angle of 30° as follows:

\displaystyle \tan 30^\circ=\frac{\text{opposite leg}}{\text{adjacent leg}}

\displaystyle \tan 30^\circ=\frac{3}{y}

Solving for y:

\displaystyle y=\frac{3}{\tan 30^\circ}

Since:

\tan 30^\circ=\frac{1}{\sqrt{3}}

\displaystyle y=3\sqrt{3}

Now applying the sine to find the hypotenuse x:

\displaystyle \sin 30^\circ=\frac{\text{opposite leg}}{\text{hypotenuse}}

\displaystyle \sin 30^\circ=\frac{3}{x}

Solving for x:

\displaystyle x=\frac{3}{\sin 30^\circ}

Since:

\sin 30^\circ=\frac{1}{2}

\displaystyle x=\frac{3}{\frac{1}{2}}

x = 6


QUESTION 1
Find the remaining sides of a 30° -60°-90° triangle if the shortest side is 3.
gungamer720
gungamer720
4,6(56 marks)
  example you can find the perimeter by addig all of its respective sides as such: (12+x)+(12+x)+(7+y)+(7+y).  adding like terms will result in   2x+2y+38    if you chose  xy+7x+12y+84, you multiplied the two sides to find the area.  if you chose  x+y+19

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