Work out the area of this triangle given the lengths of 1 sides (a) and 2 angles (A and B) using either the sine rule

We know the area of any triangle is equal to 0.5abSin(C). This means we need to find the length of side b and the angle C.First we can work out the angle C of the triangle as we know the angles in a triangle add up to 180 degrees. Say we have angle A is 35 and angle B is 70. This means angle C is 180 - (35 + 70). Next we can use the sine rule to calculate the value of side b. Say side a = 5cm. The rule is a/Sin(A) = b/Sin(B) = c/Sin(C). Substituting in the values we have we can say 5/Sin35 = b/Sin70. Rearrange to get b = 5Sin70/Sin35.
Therefore the area of the triangle = 0.5 * 5 * 5sin70/sin35 * sin 75

RA
Answered by Risha A. Maths tutor

3712 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve algebraically the simultaneous equations 3x + 2y = 15 and 2x + 4y = 10


Solve this equation: 5x-4=3x+7


Find the centre and radius of the circle with equation: x^2 + y^2 -4x +8y = 5, and determine whether the point (7,-4) lies on the circle.


What do I do when quadratic equations aren't written in the standard format ax^2 + bx + c = 0 ?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning