A triangle has sides A, B, and C. The angle between sides A and B is (pi)/2. If side C has a length of 23 and the angle between sides B and C is pi/12, what is the length of side A?

3 Answers
Narad T.
Jul 15, 2017

The length of side A is =5.95

Explanation:

enter image source here

The angle hatC=1/2pi

The angle hatA=1/12pi

The side c=23

The side a=?

We apply the sine rule to the triangle DeltaABC

a/sin hat(A)=c/sin hat(C)

a=c*sin hat (A)/sin hat (C)

=23*sin(1/12pi)/sin(1/2pi)

=5.95

HCH
Jul 15, 2017

a=5.9528units

Explanation:

Use the Sine Law
sinA/a=sinB/b=sinC/c

Angle between A and B = angle C =pi/2
Angle between B and C = angle A =pi/12
c=23 units

sin(pi/12)/a=sin(pi/2)/23

(23sin(pi/12))/sin(pi/2)=a

a=5.9528units

Rutik Tupe
Jul 15, 2017

5.8 units

Explanation:

By your question its clearly identified that its a right angled triangle with side c as its hypotenuse.

The value of :-

sin(pi/12) = (sqrt(3) - 1)/(2sqrt(2))
sqrt3 =1.71
sqrt2 = 1.41

is to be remembered

So,
A/23 = (sqrt(3) - 1)/(2sqrt(2))

By calculating we get,
A = 5.8 units

Related questions
See all questions in The Law of Sines
Impact of this question
5501 views around the world
You can reuse this answer
Creative Commons License