Question

The base of a parallelogram is 154 cm and its diagonals make angles of 28 and 43 with the base. Find the length of the longer diagonal. Answer with text and/or attachments: + Add attachments

Answer 1

Answer:we have triangle ABC,

where AB = 154 cm is base,

BC, AC are halves of diagonals,

∠

�

�

�

=

�

=

28

°

,

∠

�

�

�

=

�

=

43

°

∠BAC=α=28°,∠ABC=β=43°

∠

�

�

�

=

�

=

180

°

−

28

°

−

43

°

=

109

°

∠ACB=γ=180°−28°−43°=109°

Then:

�

�

�

�

�

�

=

�

�

�

�

�

�

=

�

�

�

�

�

�

BC

sinα

​

=

AC

sinβ

​

=

AB

sinγ

​

�

�

=

�

�

�

�

�

�

/

�

�

�

�

=

154

�

�

�

43

°

/

�

�

�

109

°

=

111.08

AC=ABsinβ/sinγ=154sin43°/sin109°=111.08 cm

�

�

=

�

�

�

�

�

�

/

�

�

�

�

=

154

�

�

�

28

°

/

�

�

�

109

°

=

76.46

BC=ABsinα/sinγ=154sin28°/sin109°=76.46 cm

So, the length of the longer diagonal:

2

�

�

=

2

⋅

111.08

=

222.16

2AC=2⋅111.08=222.16 cm

Explanation: