# What is the area triangle ABC if AB= 48cm, BC = 20cm and angle A=53 degrees?

May 10, 2016

There seems to be a problem with this question, the triangle is impossible.

#### Explanation:

To find the area of a triangle, there must be an indication of the height (indicated by a right-angle).

However, if this is not given there is a trig formula for area.
In order to use it, there must be three pieces of information available.... 2 sides and the angle between them (the included angle).

Neither of these can be done yet, so we have to use the sin rule to find another angle. Draw a sketch of the triangle!!

$\sin \frac{C}{c} = \sin \frac{A}{a} \text{ } \Rightarrow \sin \frac{C}{48} = \sin \frac{53}{20}$

$\sin C = \frac{48 \sin 53}{20} = 1.917$

This is an impossible answer for sine. There is a problem with the question - this triangle is impossible.