To determine the measure of each of the three angles where the fence walls meet in Su's triangular pen, we can use the law of cosines.
The law of cosines states:
c^2 = a^2 + b^2 - 2ab*cos(C)
Where c is the side opposite angle C, and a and b are the lengths of the other two sides.
Given that the sides of the triangle are 26.6 ft, 16.6 ft, and 31.6 ft, we can label them as follows:
a = 26.6 ft
b = 16.6 ft
c = 31.6 ft
Now, we can calculate the measure of each angle:
For angle A:
c^2 = a^2 + b^2 - 2ab*cos(C)
(31.6)^2 = (26.6)^2 + (16.6)^2 - 2(26.6)(16.6)*cos(A)
999.36 = 707.56 + 275.56 - 884.48*cos(A)
999.36 = 983.12 - 884.48*cos(A)
16.24 = -884.48*cos(A)
cos(A) = -0.018
A = cos^-1(-0.018) = 91.3 degrees (rounded to one decimal place)
For angle B:
c^2 = a^2 + b^2 - 2ab*cos(C)
(26.6)^2 = (31.6)^2 + (16.6)^2 - 2(31.6)(16.6)*cos(B)
707.56 = 998.56 + 275.56 - 1051.36*cos(B)
707.56 = 1274.12 - 1051.36*cos(B)
566.56 = -1051.36*cos(B)
cos(B) = -0.539
B = cos^-1(-0.539) = 127.5 degrees (rounded to one decimal place)
For angle C:
c^2 = a^2 + b^2 - 2ab*cos(C)
(16.6)^2 = (31.6)^2 + (26.6)^2 - 2(31.6)(26.6)*cos(C)
275.56 = 998.56 + 707.56 - 1676.16*cos(C)
275.56 = 1706.12 - 1676.16*cos(C)
-1430.56 = -1676.16*cos(C)
cos(C) = 0.852
C = cos^-1(0.852) = 32.2 degrees (rounded to one decimal place)
Therefore, the measure of each of the three angles where the fence walls meet in Su's triangular pen are:
Angle A = 91.3 degrees
Angle B = 127.5 degrees
Angle C = 32.2 degrees
Su is building a pen for her donkeys, and she wants it to be in the shape of a triangle. She plans the fences to measure 26.6 ft, 16.6 ft and 31.6 ft. Determine the measure of each of the three angles where the fence walls meet? Express each angle measure to the nearest degree. Describe in detail how to do it
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1 answer