Question

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

Answer 1

Explanation:

It is given that in ΔABC,
`AB=5√(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√(2){*}(1)/(2)=BC{*}(1)/(√(2))`

`(5)/(2)=(BC)/(2)`

`BC=5`

Again using sine law, we have

`BCsinA=ACsinB`

Substituting the values, we have

`5{*}(1)/(√(2))=AC{*}sin105`

`(5)/(1.365)=AC`

`AC=3.66`

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

Answer 2

BC = 5 m

AC = 3.66 m

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