Question-206804

Question Number 206804 by mr W last updated on 25/Apr/24

Answered by mr W last updated on 26/Apr/24

Commented by mr W last updated on 26/Apr/24

\frac{3 y}{5 y} \times \frac{a}{b} \times \frac{c + d}{d} = 1

\Rightarrow \frac{c}{d} = \frac{5 b - 3 a}{3 a} \dots (i)

\frac{x}{3 x} \times \frac{d}{c} \times \frac{b + a}{a} = 1

\Rightarrow \frac{c}{d} = \frac{a + b}{3 a} \dots (i i)

\Rightarrow a + b = 5 b - 3 a

\Rightarrow a = b

\frac{B A}{B C} = \frac{b}{a} = 1 \Rightarrow B A = B C

\Rightarrow Δ A B D \equiv Δ C B D

\Rightarrow ∠ A = ∠ C = \frac{180 - 2 \times 35}{2} = 55 ° ✓

Answered by A5T last updated on 26/Apr/24

Commented by mr W last updated on 26/Apr/24

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Commented by A5T last updated on 26/Apr/24

\frac{s i n θ}{3 x} = \frac{s i n 35}{3 y} \Rightarrow s i n θ = \frac{x s i n 35}{y}

\frac{s i n θ}{A B} = \frac{s i n 70}{8 y} \Rightarrow A B = \frac{4 x}{c o s 35}

{B C}^{2} = 16 x^{2} + \frac{16 x^{2}}{{c o s}^{2} 35} - 32 x^{2} = \frac{16 x^{2}}{{c o s}^{2} 35} - 16 x^{2}

\Rightarrow B C = 4 x \sqrt{\frac{1}{{c o s}^{2} 35} - 1} = \frac{4 x s i n 35}{c o s 35}

\frac{s i n (35 + ?)}{A B} = \frac{s i n 35}{B C} \Rightarrow \frac{s i n (35 + ?) c o s 35}{4 x} = \frac{c o s 35 s i n 35}{4 x s i n 35}

s i n (35 + ?) = 1 \Rightarrow ? = 55 °

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