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

User Eric Harms
by
8.3k points

2 Answers

4 votes

Answer:

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.

Given: △ABC, AB=5 2 m∠A=45°, m∠C=30° Find: BC and AC-example-1
User Fatou
by
8.7k points
3 votes

Answer:

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

User Chris Visser
by
8.0k points

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