A triangle has sides A,B, and C. If the angle between sides A and B is (3pi)/8, the angle between sides B and C is pi/4, and the length of B is 7, what is the area of the triangle?
1 Answer
≈ 17.32 square units
Explanation:
The area of a triangle can be calculated using
1/2ab sintheta
wheretheta" is the angle between a and b " In this triangle , only know the length of one side B. Require to find the length of A or C.
This can be done using the
color(blue)" sine rule "
A/sinA = B/sinB = C/sinC
where the angles A , B and C on the denominator represent the angles opposite the corresponding sides A , B and C.
color(red)" Calculating the length of side C" using
B/sinB = C/sinC Before using this, require the size of angle B
The sum of the 3 angles in a triangle
= pi angle B
= [pi - ((3pi)/8 + pi/4 )] = pi - (5pi)/8 = (3pi)/8 Now angle B = angle C hence side B = sideC = 7
In this question B = C = 7 and
theta = pi/4
"area" = 1/2xxBxxCsintheta = 1/2xx7xx7xxsin(pi/4) ≈ 17.32
