In ΔDEF, the measure of ∠F=90°, FD = 3.3 feet, and DE = 3.9 feet. Find the measure of ∠D to the nearest degree.

Question

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Answer 1

side opposite angle D is square root of (3.9^2 -3.3^2) = about 2.0785

use law of sines

sinD/2.08 = sin90/3.9

sinD = 2.08/3.9

D = arcsin(2.08/3.9) = about 32.23 degrees

= about 32 degrees

angle opposite smallest side is the smallest angle

sides 3.9 - 3.3 - 2.08

angles 90 - 58 - 32