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Solnce55 [7]
3 years ago
6

What color is the grass

Mathematics
1 answer:
djverab [1.8K]3 years ago
4 0

what color is the grass

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6 dogs are there who ate the biscuits

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here

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Given: △ABC, m∠A=60° m∠C=45°, AB=8 Find: Perimeter of △ABC, Area of △ABC
jarptica [38.1K]

We are given

△ABC, m∠A=60° m∠C=45°, AB=8

Firstly, we will find all angles and sides

Calculation of angle B:

we know that sum of all angles is 180

m∠A+ m∠B+m∠C=180

we can plug values

60°+ m∠B+45°=180

m∠B=75°

Calculation of BC:

we can use law of sines

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

now, we can plug values

\frac{8}{sin(45)}=\frac{BC}{sin(60)}

BC=\frac{8}{sin(45)} \times sin(60)

BC=9.798

Calculation of AC:

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

now, we can plug values

\frac{8}{sin(45)}=\frac{AC}{sin(75)}

AC=\frac{8}{sin(45)} \times sin(75)

AC=10.928

Perimeter:

p=AB+BC+AC

we can plug values

p=10.928+8+9.798

p=28.726

Area:

we can use formula

A=\frac{1}{2}AB \times AC \times sin(A)

now, we can plug values

A=\frac{1}{2}8 \times 10.928 \times sin(60)

A=37.85570...............Answer

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