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Vera_Pavlovna [14]
3 years ago
10

A triangle has a hypotenuse of 2.9ft and a leg of 2.6ft. Find the smallest angle.

Mathematics
1 answer:
OleMash [197]3 years ago
8 0

Answer:

 Lowest angle of the triangle with hypotenuse of 2.9ft and a leg of 2.6ft is   26.29°.

Explanation:

 A triangle has a hypotenuse of 2.9ft and a leg of 2.6ft

 We  have smallest angle = Angle C

 We have, Cos C = AC/BC

                            = 2.6/2.9

                           = 0.897

                      C = 26.29°

So lowest angle of the triangle with hypotenuse of 2.9ft and a leg of 2.6ft is   26.29°.

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<h2>\large\mathfrak{{\pmb{\underline{\red{Given}}{\red{:}}}}}</h2>
  • ∠RSU and ∠USV are complementary angles
  • ∠RSU = (4x – 15)°
  • ∠USV = 20°

<h2>\large\mathfrak{{\pmb{\underline{\color{red}{To~find}}{\color{red}{:}}}}}</h2>
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<h2>\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}</h2>
  • ∠RSU and ∠USV are complementary angles

\sf\implies{ \angle RSU + \angle USV = 90 \degree }

\sf\implies{ (4x-15) + 20 = 90 }

\sf\implies{ 4x-15+20=90}

\sf\implies{4x+5=90}

\sf\implies{4x=90-5}

\sf\implies{4x=85}

\sf\implies{x={\dfrac{85}{4}}}

\sf\implies{ {\orange{\underline{\boxed{\sf{\pmb{x=21.25}}}}}}}

<h2>\large\mathfrak{\therefore{\pmb{\underline{\color{gold}{Required~answer}}{\color{gold}{:}}}}}</h2>
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