Question

a parallelogram has side lenghts 20 cm and 25 cm. the diagonal opposite the obtuse angle measures 38 cm. what is the measure of the obtuse angle?

Answer 1

Explanation:

1. draw the parallelogram with side 20cm and 25cm respectively and also the diagonal as well.

2.Clearly it forms a triangle in the parallelogram with three known lengths of side.

3.Using the cosine rule : c^2=b^2+c^2 -2bc cos c to find the obtuse angle.

Answer 2

9514 1404 393

Answer:

114.8°

Explanation:

The angles can be found using the Law of Cosines. It tells you ...

c² = a² +b² -2ab·cos(C)

Then angle C can be found to be ...

C = arccos((a² +b² -c²)/(2ab)) = arccos((20² +25² -38²)/(2·20·25))

C = arccos(-419/1000) ≈ 114.77°

The measure of the obtuse angle is about 114.8°.