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beks73 [17]
3 years ago
14

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

Mathematics
1 answer:
hichkok12 [17]3 years ago
4 0

Answer:

Part a) BC=10\ units

Part b) AC=13.66\ units

Step-by-step explanation:

step 1

Find the length side BC

Applying the law of sines

we know that

\frac{AB}{sin(C)}=\frac{BC}{sin(A)}

we have

AB=5\sqrt{2}\ units

A=45^o

C=30^o

substitute

\frac{5\sqrt{2}}{sin(30^o)}=\frac{BC}{sin(45^o)}

solve for BC

BC=\frac{5\sqrt{2}}{sin(30^o)}(sin(45^o))

BC=10\ units

step 2

Find the measure of angle B

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

so

m\angle A+m\angle B+m\angle C=180^o

substitute the given values

45^o+m\angle B+30^o=180^o

75^o+m\angle B=180^o

m\angle B=180^o-75^o

m\angle B=105^o

step 3

Find the length side AC

Applying the law of sines

we know that

\frac{AB}{sin(C)}=\frac{AC}{sin(B)}

we have

AB=5\sqrt{2}\ units

A=45^o

B=105^o

substitute

\frac{5\sqrt{2}}{sin(30^o)}=\frac{AC}{sin(105^o)}

solve for AC

AC=\frac{5\sqrt{2}}{sin(30^o)}(sin(105^o))

AC=13.66\ units

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