Question

Solve each of the following problems. 1. A parallelogram has side lengths 20 cm and 25 cm. The diagonal opposite the obtuse angle measures 38 cm. What is 2 the measure of the obtuse angle?​

Answer 1

The measure of the obtuse angle of the parallelogram is 114.77°.

Given: A parallelogram with sides 20 cm and 25 cm.

         The diagonal opposite the obtuse angle is 38 cm.

         AC = 38, AB = 25, CB = 20.

To Find: The measure of the obtuse angle

Solution:

Let the obtuse angle be ∠B.

Thus, using the cosine law,

AC² = AB² + CB² - 2 × AB × CB × cos B

38² = 25² + 20² - 2×25×20 × cos B

1000 cos B = 1025 - 1444

cos B = - 0. 419

∴ ∠B = cos^-1 ( - 0.419 )

∠B = 114.77°

The measure of the obtuse angle of the parallelogram is 114.77°

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Answer 2

The obtuse angle will measure 114.7°.

Given,

One side of the parallelogram measure is= 20 cm.

Another side of the parallelogram measure is= 25 cm.

The diagonal measure= 38 cm.

To find:

The measure of the obtuse angle.

Solution:

Suppose the obtuse angle ∠a.

The formula is,

$AC^{2} = AB^{2} + CB^{2}$- 2 × AB × CB × Cos ∠a

So, according to the cosine rule,

$38^{2} = 25^{2} + 20^{2}$ - 2× 25 ×20 × Cos ∠a

1000Cos ∠a = -419

Cos ∠a = -0.419

∠a= $cos^{-1}$ (-0.419)

∠a= 114.7°

Hence, the answer is 114.7°.