Question

If the sides of a triangle are in the ratio 2: root 6: root 3 +1

Answer 1

Answer:

A = 45° , B = 30°   & C = 105°

Step-by-step explanation:

Question should be if the he sides of a triangle are in the ratio 2: root 2: root 3 +1 then find the angles

let say

a = 2k

b = √2k

c = (√3 + 1)k

c² = a² + b² - 2abCosC

(√3 + 1)k² = 2k² + (√2k)² - 2(2k)(√2k)CosC

=> 3 + 1 + 2√3 = 4 + 2 - 4√2CosC

=> 2√3 - 2 = - 4√2CosC

=> CosC = (1 - √3)/2√2

=> C = 105°

SinC = √1 - Cos²C  = (1 + √3)/2√2

a/SinA  = b/SinB  = c/SinC

=> 2k/SinA  =  √2k/SinB  = (√3 + 1)k/SinC

=>  2/SinA  =  √2/SinB  = (√3 + 1)/((1 + √3)/2√2)

=> 2/SinA  =  √2/SinB   = 2√2

=> SinA = 1/√2  => A = 45°

SinB = 1/2  => B = 30°

A = 45° , B = 30°   & C = 105°

Answer 2

Answer

A=45°

B=60°

c=75°

Step-by-step explanation:

sorry amitnrw your answer is wrong