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3 years ago

Here's a better picture

Mathematics

1 answer:

schepotkina [342]3 years ago

7 0

1) 3/5=9/x (cross multiply)
3x=5(9)
3x=45
x=15

2) 2/4=x/12 (cross multiply)
 2(12)=4x
 24=4x
 6=x

3) 10/x=5/9 (cross multiply)
10(9)=5x
90=5x
18=x

4) 5/6=x/18
5(18)=6x
90=6x
x=15

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Answer:

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Given:

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Solution:

Using angle sum property in a triangle:

m∠A + m∠B + m∠C = 180°

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As per Sine Rule:

$\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}$

Where

$a$ is the side opposite to $\angle A$

$b$ is the side opposite to $\angle B$

$c$ is the side opposite to $\angle C$

$\dfrac{BC}{sin60^\circ} = \dfrac{AC}{sin 75^\circ} = \dfrac{AB}{sin 45^\circ} \\\Rightarrow \dfrac{BC}{\frac{\sqrt3}{2}} = \dfrac{9}{\frac{1}{\sqrt2}} \\\Rightarrow BC = 12.73\times 0.87 \\\Rightarrow BC = 11.08$

$\Rightarrow \dfrac{AC}{0.96} = \dfrac{9}{\frac{1}{\sqrt2}} \\\Rightarrow AC = 12.73\times 0.96 \\\Rightarrow AC = 12.22$

Perimeter of △ABC = AB + BC + AC = 9 + 11.08 + 12.22 = 32.3

Area of a triangle is given as:

$\dfrac{1}2\times ab sin(angle\ between\ a\ and\ b)$

$\Rightarrow \dfrac{1}{2}\times AB\times AC\times sinA\\\Rightarrow 9\times 12.22\times sin 60\\\Rightarrow \bold{95.24}$

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