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A bridge is supported by triangular braces. If the sides of each brace have lengths 63 ft, 46 ft, and 40 ft, find the measure of the angle opposite the 46 ft side.

A bridge is supported by triangular braces If the sides of each brace have lengths 63 ft 46 ft and 40 ft find the measure of the angle opposite the 46 ft side class=

Respuesta :

calculista

Answer:

[tex]46.76\°[/tex]

Step-by-step explanation:

we know that

Applying the law of cosines

[tex]c^{2} =a^{2}+b^{2}-2(a)(b)cos (C)[/tex]

we have

[tex]a=63\ ft[/tex]

[tex]b=40\ ft[/tex]

[tex]c=46\ ft[/tex]

The measure of angle C is the angle opposite the 46 ft side

substitute the value

[tex]46^{2} =63^{2}+40^{2}-2(63)(40)cos (C)[/tex]

[tex]cos (C)=[63^{2}+40^{2}-46^{2}]/(2(63)(40))=0.6851[/tex]

[tex]C=arccos (0.6851)=46.76\°[/tex]

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