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2 years ago

Select the correct answer. What is the value of X in the triangle?

Mathematics

2 answers:

arlik [135]2 years ago

5 0

Answer:

Step-by-step explanation:

The sum of all the angles of a triangle always equals 180 degrees. Write down the difference you found when subtracting the sum of the two angles from 180 degrees. This is the value of X.

mash [69]2 years ago

4 0

^^ she is right so yeah lol

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Given: △ABC, m∠A=60°

Anon25 [30]

Answer:

Perimeter = 32.3

Area = 95.24

Step-by-step explanation:

Given:

△ABC, m∠A=60°

m∠C=45°, AB = 9

To find:

Perimeter of △ABC

Area of △ABC

Solution:

Using angle sum property in a triangle:

m∠A + m∠B + m∠C = 180°

m∠B = 180° - 45° - 60° = 75°

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 = <em>32.3</em>

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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Answer:

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