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For the right triangle find the missing quantity indicated below in the picture, round to the nearest hundredth as needed.

For the right triangle find the missing quantity indicated below in the picture, round-example-1

1 Answer

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Explanation:

remember, the sum of all angles in a triangle is 180°.

and then remember the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

a, b, c are the sides of the triangle, A, B, C are the corresponding opposite angles for the sides.

the third angle (opposite of a) is

180 - 90 - 76°49' = 90 - 76 49/60° =

= 90 - 76.81666666...° = 13.18333333...°

as 1 degree = 60 arc minutes.

and so,

a/sin(13.18333333...) = 42.42/sin(76.81666666...)

a = 42.42×sin(13.18333333...)/sin(76.81666666...) =

= 9.936503757... ≈ 9.94 km

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