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. In a 30°-60-90° triangle, the hypotenuse is 7 yards long.Find the exact lengths of the legs?

User KBurchfiel
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1 Answer

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ANSWER

The lengths of the legs of the triangle are 6.06 yards and 3.6 yards.

Step-by-step explanation

First, let us make a sketch of the problem:

To find the length of the legs, we have to apply trigonometric ratios SOHCAHTOA.

We have that:


\sin (60)=\frac{\text{opposite}}{\text{hypotenuse}}

From the diagram:


\begin{gathered} \sin (60)=(x)/(7) \\ \Rightarrow x=7\cdot\sin (60) \\ x\approx6.06\text{ yds} \end{gathered}

We also have that:


\sin (30)=\frac{\text{opposite}}{\text{hypotenuse}}

From the diagram:


\begin{gathered} \sin (30)=(y)/(7) \\ \Rightarrow y=7\cdot\sin (30) \\ y=3.5\text{ yds} \end{gathered}

The lengths of the legs of the triangle are 6.06 yards and 3.5 yards.

. In a 30°-60-90° triangle, the hypotenuse is 7 yards long.Find the exact lengths-example-1
User Paul Woidke
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4.0k points