SOLUTION: If a right triangle has lengths of 10, 24 and 26 feet, what is the measurement of the smallest angle?
Round your answer to the nearest whole angle (Points : 1)
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Question 973914: If a right triangle has lengths of 10, 24 and 26 feet, what is the measurement of the smallest angle?
Round your answer to the nearest whole angle (Points : 1)
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
a: 10
b: 24
c: 26
Using the Law of Cosines, first we find angle A:
cos A = (b^2 + c^2 − a^2) / 2bc
cos A = (24^2 + 26^2 − 10^2) / (2×24×26)
cos A = (576 + 676 − 100) / 1248
cos A = 0.92
A = cos^−1(0.92)
A = 23.07°
A = 23.1° to one decimal place.
Now let's find B:
cos B = (c^2 + a^2 − b^2)/2ca
cos B = (676 + 100 − 576)/(2×26×10)
cos B = (676 + 100 − 576)/ 520
cos B = 0.6875
B = cos^−1(0.3846)
B = 67.38°
B = 67.4° to one decimal place
Finally C: The angles of EVERY triangle add up to 180. Thus:
180-23.1-67.4= 89.5 is your angle C.
Answer:
A = 23.1°
B = 67.4°
C = 89.5°
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