Question

Solve the triangle with sides a and b are 150 cm and 200 cm, respectively, and angle A is 40°

Answer 1

c ≈ 75.9 , ∠B = 19° , ∠C = 121°  or c ≈ 230.5 , ∠B = 81° , ∠C = 59° in triangle with sides a and b are 150 cm and 200 cm respectively and angle A is 40°

Given:

• ΔABC with sides a , b
• a=150 cm
• b = 200 cm
• ∠A = 40°

To Find :

• side c
• ∠B
• ∠C      

Law of cosine:

In any ΔABC , with side lengths a , b  and c opposite angles A , B and C , respectively then:

a² = b² + c² -2bc cosA

b² = a² + c² -2ac cosB

c² = a² + b² -2ab cosC

Step 1:

Apply cosine law and substitute the values.

150² = 200² + c² - 2(200)c cos(40°)

Step 2:

Solve for c:

c ≈ 75.9 , c ≈ 230.5

Hence two triangles are possible

Step 3:

Use sine law of triangle to find angle B and C

$\dfrac{\sin A}{a} =\dfrac{\sin B}{b} =\dfrac{\sin C}{c}$

Step 4:

Substitute the values and  find angles for both the triangles

Result are

Triangle one

c ≈ 75.9 , ∠B = 19° , ∠C = 121°

Another Triangle

c ≈ 230.5 , ∠B = 81° , ∠C = 59°

c ≈ 75.9 , ∠B = 19° , ∠C = 121°  or c ≈ 230.5 , ∠B = 81° , ∠C = 59° in triangle with sides a and b are 150 cm and 200 cm respectively and angle A is 40°