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What is the area of this triangle?
Enter your
answer as a decimal in the box. Round only your final
answer to the nearest tenth. 8, 28, 7

What is the area of this triangle Enter your answer as a decimal in the box Round only your final answer to the nearest tenth 8 28 7 class=

Respuesta :

semsee45

Answer:

13.1 cm² (nearest tenth)

Step-by-step explanation:

Use the sine rule for area of a triangle with 2 sides and an included angle (SAS).

Sine rule for area

[tex]\textsf{Area ABC}=\dfrac12ab \sin C[/tex]

(where [tex]a[/tex] and [tex]b[/tex] are the side lengths and [tex]C[/tex] is the included angle)

Given:

  • [tex]a[/tex] = 8 cm
  • [tex]b[/tex] = 7 cm
  • [tex]C[/tex] = 28°

[tex]\implies \textsf{Area}=\dfrac12\cdot 8 \cdot 7 \cdot\sin (28\textdegree)[/tex]

               [tex]=13.14520376...[/tex]

               [tex]= 13.1 \textsf{ cm}^2 \textsf{ (nearest tenth)}[/tex]

Use sine rule

Area:-

[tex]\\ \sf\longmapsto \dfrac{1}{2}Base\times Height sin\theta[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{2}(8)(7)sin28[/tex]

[tex]\\ \sf\longmapsto 28sin28[/tex]

[tex]\\ \sf\longmapsto 13.1cm^2(Approx)[/tex]

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