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Use the Pythagorean Theorem to find the missing leg of the right triangle and the. Identify the trig ratios

Use the Pythagorean Theorem to find the missing leg of the right triangle and the-example-1
User JoHa
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1 Answer

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The Pythagorean theorem states:


c^2=a^2+b^2

where a and b are the legs and c is the hypotenuse of a right triangle.

In triangle EDF, DE = 29 is the hypotenuse, and FE = 20 and DF are the legs. Substituting this information into the formula and solving for DF, we get:


\begin{gathered} DE^2=FE^2+DF^2 \\ 29^2=20^2+DF^2 \\ 841=400+DF^2 \\ 841-400=DF^2 \\ \sqrt[]{441}=DF \\ 21=DF \end{gathered}

Sine formula


\sin (angle)=\frac{\text{opposite side}}{hypotenuse}

Considering angle D, the opposite side is FE, then:


\begin{gathered} \sin D=(FE)/(DE) \\ \sin D=(20)/(29) \end{gathered}

Considering angle E, the opposite side is DF, then:


\begin{gathered} \sin E=(DF)/(DE) \\ \sin E=(21)/(29) \end{gathered}

Cosine formula


\cos (angle)=\frac{\text{adjacent side}}{hypotenuse}

Considering angle D, the adjacent side is DF, then:


\begin{gathered} \cos D=(DF)/(DE) \\ \cos D=(21)/(29) \end{gathered}

Considering angle E, the adjacent side is FE, then:


\begin{gathered} \cos E=(FE)/(DE) \\ \cos E=(20)/(29) \end{gathered}

Tangent formula


\tan (angle)=\frac{\text{opposite side}}{adjacent\text{ side}}

Considering angle D, the opposite side is FE and the adjacent side is DF, then:


\begin{gathered} \tan D=(FE)/(DF) \\ \tan D=(20)/(21) \end{gathered}

Considering angle E, the opposite side is DF and the adjacent side is FE, then:


\begin{gathered} \tan E=(DF)/(FE) \\ \tan E=(21)/(20) \end{gathered}

User Milind Morey
by
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