Question

Given: △ABC, AB=5 2 m∠A=45°, m∠C=30° Find: BC and AC

Answer 1

Answer:

Step-by-step explanation:

It is given  that in ΔABC, $AB=5\sqrt{2}$, ∠A=45°, ∠C=30°.

Now, using the angle sum property in ΔABC, we have

${\angle}A+{\angle}B+{\angle}C=180$

$45+{\angle}B+30=180$

${\angle}B=105^{\circ}$

Using the sine law, we have

$ABsinC=BCsinA$

Substituting the given values, we have

$5\sqrt{2}{\times}\frac{1}{2}=BC{\times}\frac{1}{\sqrt{2}}$

$\frac{5}{2}=\frac{BC}{2}$

$BC=5$

Again using sine law, we have

$BCsinA=ACsinB$

Substituting the values, we have

$5{\times}\frac{1}{\sqrt{2}}=AC{\times}sin105$

$\frac{5}{1.365}=AC$

$AC=3.66$

Therefore, the value of BC  and AC are $5$ and $3.66$.

Answer 2

Answer:

BC = 5 m

AC = 3.66 m

Step-by-step explanation:

Using the sin rule,

AB×sin C = BC×Sin A

5√2 × Sin 30 =  a sin 45

3.5355 = BC sin 45

BC = 3.5355/sin 45

    = 5 m

AC × sin 105 = 5√2 × sin 30

AC = 3.5355/sin 105

      = 3.66 m