Solve the triangle. B = 36°, a = 38, c = 17
Solution:
The information provided in the problem statement is summarised in the figure below:
By solving the triangle it implies that the values of ∠A , ∠C and side b have to be determined.
Therefore to obtain these values a perpendicular is dropped from vertex A on to the side BC as shown in the diagram below:
We know that.
Cos36° = BD/AB And AB = c = 17
Cos36° = 0.8089
Therefore.
BD = ABcos36°
= 17cos36°
= 17( 0.8089)
= 13.75
Therefore we can now determine DC from the relationship
DC = BC - BD
= 38 - 13.75
= 24.25
We also know sin36° = AD/AB
AB = 17 and sin 36°= 0.588 AD = ABsin36°
= (17)(0.588)
= 9.996
Now
Tan C° = AD/DC
= 9.996/24.25
=0.4122
C° = 22.39
The Cosine of angle C is given as cosC° = DC/AC
C° = 22.39 and DC = 24.25
Therefore
AC = DC/cos22.39°
cos 22.39° = 0.9245
Therefore
AC = 24.25/0.9245
= 26.23
∠A = 180° - 36° - 22.39°
= 121.61°
Therefore all the parameters of the triangle are obtained as follows:
a = 38; c = 17; b = 26.23; ∠A = 121.61°; ∠B = 36° and ∠C = 22.39°
Solve the triangle. B = 36°, a = 38, c = 17
Summary:
Solving the given triangle with ∠B = 36°, a = 38, c = 17 we have b = 26.23; ∠A = 121.61°; and ∠C = 22.39°.
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