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,

$\frac{\sin A}{a} =\frac{\sin B}{b}$

$\frac{\sin 35^\circ}{5.2} =\frac{\sin B}{7}$

Multiply by 7 on both sides.

$\frac{0.5735}{5.2}\times 7 =\sin B$

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°.