Clarify (Question:361856.0)

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TRINA DAS

· started a discussion

· 1 Months ago

Clarify (Question:361856.0)

How does this line come?
Area of ABC = 1/2×AB×BC×sin(θ)

Question:

In the given figure, triangle ABC is drawn such that AB is tangent to a circle at A whose radius is 10cm and BC passes through centre of the circle. Point C lies on the circle. IF BC=36 cm and AB = 24cm, then what is the area (in cm²) of triangle ABC?

Options:

134.5

148

166.15

180

Solution:

Let O be the centre of a circle and ∠ABC=θ

OC =OA = 10cm

BC =36 cm

AB =24 cm

OB =BC-OC = 36 -10 = 26 cm

In $Δ$ OAB,

$\begin{matrix} c o s (A B O) = c o s θ = \frac{A B}{O B} = \frac{24}{26} = \frac{12}{13} \\ ∴ s i n θ = \sqrt{1 - {(\frac{12}{13})}^{2}} = \frac{5}{13} \end{matrix}$

Area of ABC = $\frac{1}{2} \times A B \times B C \times s i n (θ)$

= $\frac{1}{2} \times 24 \times 36 \times \frac{5}{13} = 166.15 c m^{2}$

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Clarify (Question:361856.0)

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