Answer:
The values of BC and AC will be: BC= 9.99, AC = 6.78
Step-by-step explanation:
As the given triangle is △ABC:
where AB = 5√2, m∠A=45°, m∠C=30°
As the sum of measure of angles of a triangle will be 180°, so m∠B will be 105° which can be calculated by as:
m∠A + m∠B + m∠C = 180°
45° + m∠B + 30 = 180°
m∠B = 105°
As The Law of Sines (or Sine Rule) can be used in order to determine BC and AC.
[tex]\frac{a}{sin A}[/tex] = [tex]\frac{b}{sin B}[/tex] = [tex]\frac{c}{sin C}[/tex]
So,
a×sin C = c×sin A
BC×sin C = AB×sin A
(BC) sin 30 = 5√2 sin 45
BC (1/2) = 5√2 × (1/√2)
BC (1/2) = (7.07) (0.707)
BC = (4.99) (2)
BC= 9.99
Also,
a×sin B = b×sin A
BC sin B = AC sin A
5 × sin 105° = AC (sin 45°)
5 × (0.96) = AC × (1/√2)
4.8 × √2 = AC
AC = 6.78
Hence, The values of BC and AC of given △ABC will be:
BC= 9.99, AC = 6.78
Keywords: triangle
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