Question

Name r 13 EUA 18. Find the measure of angle A Date Period A 16 139° B A= 13 20 19. Solve the triangle ABC with side lengths a = 14cm, b = 9cm, c = 6cm a = A= b = B= C= C =​

Answer 1

A = 137° a = 14 cm

B = 26° b = 9 cm

C = 17° c = 6 cm

Explanation:

Cosine rule

`c^2=a^2+b^2-2ab\cos (C)`

`\implies C=\cos^(-1)\left((c^2-a^2-b^2)/(-2ab)\right)`

where:

• c is the side opposite angle C

• a and b are the sides with C as the included angle.

Given:

• a = 14 cm
• b = 9 cm
• c = 6 cm

`\implies C=\cos^(-1)\left((6^2-14^2-9^2)/(-2(14)(9))\right)`

`\implies C=\cos^(-1)\left((241)/(252)\right)`

`\implies C=16.99128694..\textdegree`

Sine Rule

`\sf (sinA)/(a)=(sinB)/(b)=(sinC)/(c)`

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

`\sf \implies (sinB)/(9)=(sin(16.991..))/(6)`

`\sf \implies B=sin^(-1)\left((9sin(16.991..))/(6)\right)=25.99797699...\textdegree`

Sum of interior angles of a triangle = 180°

⇒ ∠A + ∠B + ∠C = 180°

⇒ ∠A = 180° - 25.997...° - 16.9912...°

⇒ ∠A = 137.0107361...°