In rectangle ABCD,/AB/=9cm and diagonal /DB/=10cm.calculate ADB to the nearest degree

Answer 1

To find the angle ADB, we can use the cosine rule.

Let angle ABD be x degrees.

Using the cosine rule:
/AB/² = /AD/² + /BD/² - 2 * /AD/ * /BD/ * cos (ADB)

Plugging in the given values:
9² = /AD/² + 10² - 2 * /AD/ * 10 * cos (ADB)

81 = /AD/² + 100 - 20 * /AD/ * cos (ADB)

Rearranging the equation:
20 * /AD/ * cos (ADB) = /AD/² + 19

Simplifying:
/AD/ * (20 * cos (ADB) - /AD/ - 19) = 0

Since /AD/ cannot be zero, we can conclude that (20 * cos (ADB) - /AD/ - 19) must be zero.

So, we have:
20 * cos (ADB) - /AD/ - 19 = 0

Now, /AD/ = /AB/ * sin (ABD) = 9 * sin (x)

So, 20 * cos (ADB) - 9 * sin (x) - 19 = 0

To solve this equation, it is helpful to use a calculator or software that can solve trigonometric equations.

Using a calculator, we find that the value of x is approximately 63.24 degrees.

Therefore, the angle ADB is approximately 63.24 degrees to the nearest degree.