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Mathematics

Statement 1: The distance between B and C = 5 m.

The distance between B and C = 5 m; Solution of Right Triangles, Concise Mathematics Solutions ICSE Class 9.

Statement 2: BC = 333\sqrt{3} m.

  1. Both the statements are true.

  2. Both the statements are false.

  3. Statement 1 is true, and statement 2 is false.

  4. Statement 1 is false, and statement 2 is true.

Trigonometric Identities

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Answer

By formula,

tan θ = PerpendicularBase\dfrac{\text{Perpendicular}}{\text{Base}}

In ΔABP,

⇒tan P=ABBP⇒tan 60°=3BP⇒3=3BP⇒BP=33⇒BP=3 cm.\Rightarrow \text{tan P} = \dfrac{AB}{BP}\\[1em] \Rightarrow \text{tan 60°} = \dfrac{3}{BP}\\[1em] \Rightarrow \sqrt{3} = \dfrac{3}{BP}\\[1em] \Rightarrow BP = \dfrac{3}{\sqrt{3}}\\[1em] \Rightarrow BP = \sqrt{3}\text{ cm}.

In ΔPCD,

⇒tan P=DCPC⇒tan 30°=2PC⇒13=2PC⇒PC=23 cm.\Rightarrow \text{tan P} = \dfrac{DC}{PC}\\[1em] \Rightarrow \text{tan 30°} = \dfrac{2}{PC}\\[1em] \Rightarrow \dfrac{1}{\sqrt{3}} = \dfrac{2}{PC}\\[1em] \Rightarrow PC = 2 \sqrt{3}\text{ cm}.

From figure,

BC = BP + PC =3+23=33= \sqrt{3} + 2\sqrt{3} = 3\sqrt{3}.

∴ Statement 1 is false, and statement 2 is true.

Hence, option 4 is the correct option.

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