# Find the possible values of angle ##∠ADB##

• chwala
In summary, the conversation discusses the use of the cosine and sine rules to find the value of an angle and the length of a side in a triangle. The value of ##∠ADB## is determined to be ##48.59^0## and it is suggested to use steps instead of outcomes for a clearer explanation. It is also noted that using the LaTeX code for degrees is recommended. The issue of the given diagram not being to scale is also mentioned.
chwala
Gold Member
Homework Statement
See attached ( kindly allow me to post as it is on exam script)
Relevant Equations
Understanding of the Triangle

My take:

I got ##BC=10.25## cm, using cosine rule...no issue there. For part (b)
##BK=3cm## using sine rule i.e ##\sin 30^0 =\dfrac{BK}{6}##
Thus it follows that ##∠BDK=48.59^0## ...⇒##∠ADB=131.4^0## correct...any other approach?

Also:

##∠ADB=48.59^0## when BD is on the other side of the given perpendiculor line.

cheers guys

#### Attachments

• 1686584595716.png
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Last edited:
Seem ok to me.
'Not to scale' is an understatement....

And instead of outcomes, post steps: ##\angle ADB = \arcsin 3/4 = ...## is so much clearer !

##\LaTeX ## degrees is ^\circ : ##30^\circ##

##\ ##

chwala and SammyS
BvU said:
Seem ok to me.
'Not to scale' is an understatement....

And instead of outcomes, post steps: ##\angle ADB = \arcsin 3/4 = ...## is so much clearer !

##\LaTeX ## degrees is ^\circ : ##30^\circ##

##\ ##
@chwala ,

In case you miss @BvU 's post, it bears repeating... on all counts.

chwala

## 1. What is the given information or context for finding the angle ∠ADB?

The context typically involves a geometric figure such as a triangle or a quadrilateral with specific points labeled A, D, and B. The given information might include other angles, side lengths, or relationships between points, which can be used to determine the possible values of ∠ADB.

## 2. Are there any specific theorems or properties that can help find the angle ∠ADB?

Yes, several geometric theorems and properties can be useful, such as the Inscribed Angle Theorem, the Law of Sines, the Law of Cosines, and properties of cyclic quadrilaterals. These can help relate ∠ADB to other known angles or sides in the figure.

## 3. Can ∠ADB have multiple possible values?

Yes, depending on the geometric configuration and given information, ∠ADB can have multiple possible values. For example, if the figure is not uniquely determined or if there are symmetrical properties, there could be more than one valid measure for ∠ADB.

## 4. How do you approach solving for ∠ADB if the figure involves a circle?

If the figure involves a circle, you might use the Inscribed Angle Theorem, which states that an inscribed angle is half the measure of the intercepted arc. Additionally, properties of cyclic quadrilaterals (where opposite angles sum to 180 degrees) can also be helpful.

## 5. What steps should be taken to verify the calculated value of ∠ADB?

To verify the calculated value of ∠ADB, you should cross-check with other known angles or sides in the figure, use different geometric properties or theorems to see if they yield the same result, and ensure consistency with the given information. Drawing the figure accurately and using tools like a protractor can also help in verification.

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