Question

Finding third side of triangle given two sides and angle

Answer 1

Answer:

 To solve an SAS triangle

use The Law of Cosines to calculate the unknown side,

then use The Law of Sines to find the smaller of the other two angles,

and then use the three angles add to 180° to find the last angle.

Example 1



In this triangle we know:

angle A = 49°

b = 5

and c = 7

 

To solve the triangle we need to find side a and angles B and C.

Use The Law of Cosines to find side a first:

a2 = b2 + c2 − 2bc cosA

a2 = 52 + 72 − 2 × 5 × 7 × cos(49°)

a2 = 25 + 49 − 70 × cos(49°)

a2 = 74 − 70 × 0.6560...

a2 = 74 − 45.924... = 28.075...

a = √28.075...

a = 5.298...

a = 5.30 to 2 decimal places.

Hope it helps.....