Question

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

Answer 1

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