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2 years ago

What is the value of x

Mathematics

2 answers:

Lelu [443]2 years ago

6 0

ok so the complete measurement is 180° so youll need to subtract 116° from that and because the 2 other unknown measurements are both the same you'll just divide 116° by 2 and that's your answer

here's the formula

$(180 - 116) \div 2 = 64 \div 2 = 32$

therefore x=32°

hope this was helpful:)

Delicious77 [7]2 years ago

4 0

Answer:

Step-by-step explanation:

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What is the area of ABC?

notsponge [240]

Let D be the Intersection of Height of the Triangle and Base of the Triangle BC

From the Figure, We can notice that Triangle ADB is a Right angled Triangle.

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Given : AB = 15 and BD = 9

Substituting the values, We get :

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$:\implies$ 225 = (AD)² + 81

$:\implies$ (AD)² = 225 - 81

$:\implies$ (AD)² = 144

$:\implies$ (AD)² = (12)²

$:\implies$ AD = 12

We know that, In a Right angled Triangle :

$\bigstar\;\;\boxed{\mathsf{Tan\theta = \dfrac{Opposite\;Side}{Adjacent\;Side}}}$

Now, Consider Triangle ADC : With respect to 45° Angle, AD is the Opposite Side and DC is the Adjacent Side

$:\implies \mathsf{In\;Triangle\;ADC,\;Tan45^{\circ} = \dfrac{AD}{DC}}$

$\mathsf{:\implies 1 = \dfrac{12}{DC}}$

$:\implies$ DC = 12

$:\implies$ Total Length of the Base (BC) = BD + DC

$:\implies$ Total Length of the Base (BC) = 9 + 12

$:\implies$ Total Length of the Base (BC) = 21

We know that, Area of the Triangle is given by :

$\bigstar\;\;\boxed{\mathsf{Area = \dfrac{1}{2} \times Base \times Height}}$

In Triangle, ABC : AD is the Height and BC is the Base

$:\implies \mathsf{Area\;of\;the\;Triangle\;ABC = \dfrac{1}{2} \times BC \times AD}$

$:\implies \mathsf{Area\;of\;the\;Triangle\;ABC = \dfrac{1}{2} \times 21 \times 12}$

$:\implies \mathsf{Area\;of\;the\;Triangle\;ABC = (21 \times 6)}$

$:\implies \mathsf{Area\;of\;the\;Triangle\;ABC = 126}$

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