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Three sticks are arranged to form a right triangle. If the lengths of the three sticks are 0.47 m, 0.62 m and 0.78 m, what are the three angles of the triangle?
The angles in the triangle are 91 degrees, 53 degrees and 36 degrees respectively.
What is the cosine rule?From the cosine rule we know that;
c^2 = a^2 + b^2 - 2abcosC
Since;
a = 0.47 m
b = 0.62 m
c = 0.78 m
Then;
(0.78)^2 = (0.47)^2 + (0.62)^2 - 2(0.47 * 0.62)cosC
0.61 = 0.22 + 0.38 - 0.58 cosC
0.61 - ( 0.22 + 0.38) = - 0.58 cosC
0.01 = - 0.58 cosC
C = cos-1(0.01/-0.58)
C = 91 degrees
Using the sine rule;
b/Sin B = c/Sin C
0.62/sinB = 0.78/sin 91
0.62/Sin B = 0.78
B = sin-1 (0.62//0.78)
B = 53 degrees
Angle A is obtained from the sum of angles in a triangle;
180 - (91 + 53)
A = 36 degrees
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