Question

in an adjoining figure Angle B equal to 90 degree angle BAC is equal to BC equal to CD equal to 4 cm and area equal to 10 cm find sin theta and Cos theta​

Answer 1

Hi there,

The given question is incomplete. I have rewritten the question for you and have also attached the figure below and solved it accordingly. Hope it helps:)

Q. In in the adjoining figure angle B is equal to 90 degree, angle BAC is equal to θ degree, BC is equal to CD is equal to 4 cm and AD is equal to 10 cm. Find (i) sin theta and (ii) cos theta​.

Given:

∠B = 90°

∠BAC = θ°

BC = CD = 4 cm

AD = 10 cm

To find:

(i) sin θ

(ii) cos θ

Formula to be used:

$\boxed{Pythagoras Theorem\::\: Hypotenuse^2\:=\: Perpendicular^2\:+\:Base^2}$

$\boxed{Trigonometric \:Ratios\: of\: Triangles:}\\\\\boxed{sin\:theta = \frac{Perpendicular}{Hypotenuse} }\\\\\boxed{cos\:theta = \frac{Base}{Hypotenuse} }$

Solution:

Firstly, we will find the length of side AB of Δ ABD

AD = 10 cm

BD = BC + CD = 4 + 4 = 8 cm

Applying Pythagoras theorem in Δ ABD, we get

AD² = BD² + AB²

⇒ AB² = AD² - BD²

⇒ AB² = 10² - 8²

⇒ AB = $\sqrt{100 - 64}$

⇒ AB = $\sqrt{36}$

⇒ AB = 6 cm

Secondly, we will find the length of AC

AB = 6 cm

BC = 4 cm

Applying Pythagoras theorem in Δ ABC, we get

AC² = BC² + AB²

⇒ AC² = 4² + 6²

⇒ AC = $\sqrt{36 + 16}$

⇒ AC = $\sqrt{52}$

⇒ AC = 7.21 cm or 2√13 cm

(i) sin θ

Using the formula for sin theta in ΔABC, we have

sin θ = $\frac{BC}{AC}$

here BC = perpendicular and AC = Hypotenuse

⇒ sin θ = $\frac{4}{2\sqrt{13} }$

⇒ sin θ = $\frac{2}{\sqrt{13} }$ or 0.55

(ii) cos θ

Using the formula for cos theta in ΔABC, we have

cos θ = $\frac{AB}{AC}$

here AB = base and AC = Hypotenuse

⇒ cos θ = $\frac{6}{2\sqrt{13} }$

⇒ cos θ = $\frac{3}{\sqrt{13} }$ or 0.83

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Answer 2

Answer:

Step-by-step explanation: