Question

In ΔDEF, d = 5.3 cm, e = 2.4 cm and f=4.7 cm. Find the measure of ∠F to the nearest 10th of a degree.

Answer 1

62.5

Explanation:

Answer 2

Given:

In ΔDEF, d = 5.3 cm, e = 2.4 cm and f=4.7 cm.

To find:

The measure of ∠F to the nearest 10th of a degree.

Solution:

According to the law of cosine:

`\cos A=(b^2+c^2-a^2)/(2bc)`

In ΔDEF,

`\cos F=(d^2+e^2-f^2)/(2de)`

Putting the given values d = 5.3, e = 2.4 and f=4.7, we get

`\cos F=((5.3)^2+(2.4)^2-(4.7)^2)/(2(5.3)(2.4))`

`\cos F=(11.76)/(25.44)`

`\cos F=0.46226`

Taking cos inverse on both sides, we get

`F=\cos^(-1)(0.46226)`

`F=62.4669^\circ`

`F\approx 62.5^\circ`

Therefore, the measure of angle F is 62.5 degrees.