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3 years ago

HELP ITS URGENT Find the value of x.

Mathematics

1 answer:

saul85 [17]3 years ago

7 0

Answer:

Step-by-step explanation:

Exterior angle property:

Exterior angle of a triangle equals the sum of opposite interior angles

∠WBC = ∠D + ∠C

18x + 5 = 46 + 8x - 1

18x + 5 = 8x + 45

Subtract 5 from both sides

18x = 8x + 45 -5

18x = 8x + 40

Subtract 8x from both sides

18x - 8x = 40

10x = 40

Divide both sides by 10

x = 40/10

x = 4

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I don't need you to work it out, just theorem(s) i need to reach the answer :)

VikaD [51]

Not sure why such an old question is showing up on my feed...

Anyway, let $x=\tan^{-1}\dfrac43$ and $y=\sin^{-1}\dfrac35$ . Then we want to find the exact value of $\cos(x-y)$ .

Use the angle difference identity:

$\cos(x-y)=\cos x\cos y+\sin x\sin y$

and right away we find $\sin y=\dfrac35$ . By the Pythagorean theorem, we also find $\cos y=\dfrac45$ . (Actually, this could potentially be negative, but let's assume all angles are in the first quadrant for convenience.)

Meanwhile, if $\tan x=\dfrac43$ , then (by Pythagorean theorem) $\sec x=\dfrac53$ , so $\cos x=\dfrac35$ . And from this, $\sin x=\dfrac45$ .

So,

$\cos\left(\tan^{-1}\dfrac43-\sin^{-1}\dfrac35\right)=\dfrac35\cdot\dfrac45+\dfrac45\cdot\dfrac35=\dfrac{24}{25}$

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