Question

Please help! i cant solve it​

Answer 1

a ≈ 5.2, B ≈ 50°, C ≈ 95°

Solution:

Given data:

A = 35°, b = 7, c = 9

Using cosine law,

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

`a^(2)=7^(2)+9^(2)-2 (7)(9) \cos 35^\circ`

`a^(2)=49+81-126 (0.82)`

`a^(2)=26.68`

Taking square root on both sides.

a ≈ 5.2

Using sine law,

`$(\sin A)/(a) =(\sin B)/(b)`

`$(\sin 35^\circ)/(5.2) =(\sin B)/(7)`

Multiply by 7 on both sides.

`$(0.5735)/(5.2)* 7 =\sin B`

Switch the sides.

Sin B = 0.772

`B=\sin^(-1)0.772`

B ≈ 50°

Sum of all the angles of a triangle = 180°

A + B + C = 180°

35° + 50° + C = 180°

85° + C = 180°

C = 180° - 85°

C = 95°

Hence a ≈ 5.2, B ≈ 50°, C ≈ 95°.