Solving ASA Triangles

Example 1

In this triangle we know:

• angle A = 76°
• angle B = 34°
• and c = 9

It's easy to find angle C by using 'angles of a triangle add to 180°':

C = 180° − 76° − 34° = 70°

We can now find side a by using the Law of Sines:

asin(A) = csin(C)

asin(76°) = 9sin(70°)

a = sin(76°) ×ばつ 9sin(70°)

a = 9.29 to 2 decimal places

Similarly we can find side b by using the Law of Sines:

bsin(B) = csin(C)

bsin(34°) = 9sin(70°)

b = sin(34°) ×ばつ 9sin(70°)

b = 5.36 to 2 decimal places

Now we have completely solved the triangle: we have found all angles and sides.

Example 2

This is also an ASA triangle.

First find angle X by using 'angles of a triangle add to 180°':

X = 180° − 87° − 42° = 51°

Now find side y by using the Law of Sines:

ysin(Y) = xsin(X)

ysin(87°) = 18.9sin(51°)

y = sin(87°) ×ばつ 18.9sin(51°)

y = 24.29 to 2 decimal places.

Similarly we can find z by using the Law of Sines:

zsin(Z) = xsin(X)

zsin(42°) = 18.9sin(51°)

z = sin(42°) ×ばつ 18.9sin(51°)

z = 16.27 to 2 decimal places.

All done!

263, 3957, 264, 1543, 1544, 1545, 1561, 2372, 2373, 3958

Triangle Solving Practice The Law of Sines The Law of Cosines Solving Triangles Trigonometry Index Algebra Index