The shorter diagonal of a rhombus with a 70 degree angle is 122 cm long. How long, to the nearest centimeter, is the longer diagonal?
+128587 In a rhombus, the diagonals bisect each other as well as the the vertex angles and adjacent angles are supplementary......so assuming that the 70 degree angle is opposite the 122cm diagonal, we have
(1/2 length of the shorter diagonal) / sin (35) = (1/2 length of the longer diagonal) / sin(55)
Multiply both sides by 2
( length of the shorter diagonal) / sin (35) = ( length of the longer diagonal) / sin(55)
Multiply both sides by sin(55)
length of the longer diagonal = sin (55) (122 cm) / sin (35) = about 174 cm
Here's a 1/10 scale diagram......
+128587 In a rhombus, the diagonals bisect each other as well as the the vertex angles and adjacent angles are supplementary......so assuming that the 70 degree angle is opposite the 122cm diagonal, we have
(1/2 length of the shorter diagonal) / sin (35) = (1/2 length of the longer diagonal) / sin(55)
Multiply both sides by 2
( length of the shorter diagonal) / sin (35) = ( length of the longer diagonal) / sin(55)
Multiply both sides by sin(55)
length of the longer diagonal = sin (55) (122 cm) / sin (35) = about 174 cm
Here's a 1/10 scale diagram......
