# 1 math question ?

The legs of a right triangle measure 6 inches and 11 inches.

What is the measure of the smallest angle of the triangle?

Enter your answer, rounded to the nearest tenth of a degree, in the box.

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The legs of a right triangle measure 6 inches and 11 inches.

What is the measure of the smallest angle of the triangle?

Enter your answer, rounded to the nearest tenth of a degree, in the box.

∠α = 28.61° = 28°36'38" = 0.49935 rad

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• tan(x) = 6/11

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• Smallest angle is opposite smallest side and it is arctan(6/11) = 28.6 degrees to the nearest tenth

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• Units are [''].

Legs are AC = b = 11 and AB = c = 6.

a^2 = b^2 + c^2, ie., a^2 = 11^2 + 6^2 = 157.

Clearly, the smallest angle in the triangle will be

opposite the smaller arm which is c.

Law of cosines gives c^2 = a^2+b^2-2ab*cos(C).

ie., cos(C) = (a^2+b^2-c^2)/2ab.

Here, cos(C) = (157+121-36)/[2*11rt157] =

121/(11rt157) = (11/rt157) = 0.8778955729 and

C = arccos (0.8778955729) = 28.61045967°

= 28.6° to nearest tenth of a degree.

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