Question

For the following figure, \[\tan \mathrm{A}=1 \frac{2}{3}\] and \[\tan \mathrm{B}=\frac{1}{3}\]

Statement (1): x = 36 cm.

Statement (2): \[\tan \mathrm{A}=\frac{5}{3}=\frac{h}{9} \Rightarrow h=15\] \[\tan \mathrm{B}=\frac{h}{x+9} \Rightarrow \frac{1}{3}=\frac{15}{x+9}\]

पर्याय

• Both the statements are true.

• Both the statements are false.

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

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

Answer 1

Both the statements are true.

Explanation:

Given,

\[\tan A = 1\frac{2}{3} = \frac{5}{3}\] and \[\tan B = \frac{1}{3}.\]

From figure,

\[\Rightarrow \tan A = \frac{h}{9}\]

\[\Rightarrow \frac{5}{3} = \frac{h}{9}\]

\[\Rightarrow h = \frac{5 \times 9}{3}\]

⇒ h = 5 × 3

⇒ h = 15 cm

\[\Rightarrow \tan B = \frac{h}{x + 9}\]

\[\Rightarrow \frac{1}{3} = \frac{15}{x + 9}\]

⇒ x + 9 = 15 × 3

⇒ x + 9 = 45 

⇒ x = 45 − 9 

⇒ x = 36 cm.

∴ Both the statements are true.