rangehen
to answer
Colloquial for answering a phone call.
Das Telefon klingelt ununterbrochen, aber niemand will rangehen.
The phone keeps ringing, but nobody wants to answer it.

to answer / approach
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to answer
Colloquial for answering a phone call.
Das Telefon klingelt ununterbrochen, aber niemand will rangehen.
The phone keeps ringing, but nobody wants to answer it.

'Rangehen' is a separable verb with the prefix 'ran-'. In a main clause, the prefix stands at the end. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Das Telefon klingelt, geh doch mal ran!
The phone is ringing; go answer it!
The prefix 'ran' is a colloquial short form of 'heran'. It always expresses movement or approach toward something or someone. This basic idea appears in all meanings.
Lass uns endlich an die Arbeit rangehen.
Let's finally get started on the work.
In the meaning 'einen Anruf annehmen' (to answer a call), 'rangehen' (to answer) is very colloquial. It is used less often in formal or business situations.
Warum gehst du nicht ran? Vielleicht ist es wichtig.
Why don't you answer it? Maybe it's important.
When it is about starting a task or problem, 'rangehen' (to approach/tackle) is almost always used with the preposition 'an' and the accusative.
Wir müssen systematisch an dieses Problem rangehen.
We need to approach this problem systematically.
This meaning is used exclusively in the context of cooking. The subject of the sentence is always the food that sticks to the bottom of the pot.
Rühr bitte die Soße um, damit sie nicht rangeht.
Please stir the sauce so it doesn't stick.
to begin
'beginnen' and 'rangehen' can both mean that you start a task. 'beginnen' is more neutral and can be used for almost any action or process. 'rangehen' is colloquial and fits especially with tasks, problems, or work. It often emphasizes that you actively tackle something. In more formal situations, 'beginnen' sounds better. In casual conversations, people are more likely to say: 'Ich gehe jetzt an die Aufgabe ran' (I'm going to tackle the task now).

Der Lehrer erklärt, wie die Klasse an die schwierige Aufgabe rangehen soll.
The teacher explains how the class should approach the difficult task.
Samir beginnt am Nachmittag mit der Planung für den Ausflug.
Samir begins planning the trip in the afternoon.