Question

In triangle abc right angled at B ,AB=5cm and BC= 12cm find the values of sin A,sec A ,sin C , and sec C

Answer 1

ANSWER

Given:

AB = 5 cm, BC = 12 cm

Using Pythagoras theorem,

AC ^2 =AB ^2 +BC ^2

= 5 ^2 +12 ^2

= 25+144

= 169

AC=13.

We know that two tangents drawn to a circle from the same point that is exterior to the circle are of equal lengths.

So, AM=AQ=a

Similarly MB=BP=b and PC=CQ=c

We know

AB=a+b=5

BC=b+c=12 and

AC=a+c=13

Solving simultaneously we get a=3,b=2 and c=10

We also know that the tangent is perpendicular to the radius

Thus OMBP is a square with side b.

Hence the length of the radius of the circle inscribed in the right angled triangle is 2cm.