Question

$\huge\mathfrak\orange{Question}$

SOLVE THE QUESTION IN ATTACHMENT.

$\huge\mathfrak\blue{Spamming❌}$​

Answer 1

$\Large{\underline{\underline{\tt{\red{Solution}}}}}$

$\Large{\underline{\tt{\green{Find}}}}$

• sin x°
• cos y°
• 3tan x° - 2 sin y° + 4 cos y°

$\Large{\underline{\underline{\tt{\red{Explanation}}}}}$

Let,

∆ABC be a right triangle.

A other line AD in BC .

Then , we take here two triangle.

• Right ∆ ABC
• Rught ∆ ADC .

Where,

• <ABC = x°
• <ADC = y°
• AB = 17
• AC = 8
• BC = BD + DC = BD + 6

Now, first Calculate BD,

For this take Right ∆ABC,

Using Pythagorous Theorem

$\boxed{\underline{\tt{\red{\:(AC)^2\:=\:(BC)^2+(AC)^2}}}}$

So,

==> (17)² = (BD + BC)² + (AC)²

==> (p + 6)² = 17² - 8²

==> (p² + 36 + 12p) = 289 - 64

==> p² + 12p +36 - 225 = 0

==> p² + 12p - 189 = 0

==> p² + 21p - 9p - 189 = 0

==> p(p + 21) - 9(p + 21) = 0

==> (p + 21)(p - 9) = 0

==> ( p + 21) = 0 Or, p - 9 = 0

==> p =-21 , Or p = 9

P = -21 neglect values. , because length is not (- ve ) .

So, take

• p = 9.

So, Value of BC ,

==> BC = BD + DC

==> BC = 9 + 6

==> BC = 15

Now, Calculate AD,

==> AD² = 8² + 6²

==> AD² = 64 + 36

==> AD² = 100

==> AD = 10 .

Now, calculate trigonometry ratio .

Using Formula

★ sin x° = ( perpendicular)/(Hypotenuse)

★ cos y° = (Base)/(Hypotenuse)

★ tan x° = (Perpendicular)/(Base)

So,

==> sin x° = 8/17__________(1)

And,

==> cos y° = 6/10___________(2)

And,

==> tan x° = 8/15 __________(3)

And,

==> sin y° = 8/10________(4)

Now, Calculate value of (3tan x° - 2 sin y° + 4 cos y°)

= 3tan x° - 2 sin y° + 4 cos y°

keep all above Values,

= 3 × 8/15 - 2 × 8/10 + 4 × 6/10

= 8/5 - 8/5 + 12/5

= 12/5

Or,

= 2.4

$\Large{\underline{\underline{\tt{\green{Hence}}}}}$

• Value of sin x° = 8/17
• Value of cos y° = 6/10
• Value of (3tan x° - 2 sin y° + 4 cos y°) = 2.4

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Note:-

• Diagram Attached .

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