Question #253164

The base of the parallelogram is 154 cm and its diagonal make an angle 28° and 43° with the base. Find the length of the longer diagonal. 


1
Expert's answer
2021-10-19T14:05:32-0400

we have triangle ABC,

where AB = 154 cm is base,

BC, AC are halves of diagonals,

BAC=α=28°,ABC=β=43°\angle BAC=\alpha=28\degree,\angle ABC=\beta=43\degree

ACB=γ=180°28°43°=109°\angle ACB=\gamma=180\degree-28\degree-43\degree=109\degree


Then:

sinαBC=sinβAC=sinγAB\frac{sin\alpha}{BC}=\frac{sin\beta}{AC}=\frac{sin\gamma}{AB}


AC=ABsinβ/sinγ=154sin43°/sin109°=111.08AC=ABsin\beta/sin\gamma=154sin43\degree/sin109\degree=111.08 cm

BC=ABsinα/sinγ=154sin28°/sin109°=76.46BC=ABsin\alpha/sin\gamma=154sin28\degree/sin109\degree=76.46 cm


So, the length of the longer diagonal:

2AC=2111.08=222.162AC=2\cdot111.08=222.16 cm


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS