Question

Using the measurements given in the following figure:
(i) Find the value of sin θ and tan θ.
(ii) Write an expression for AD in terms of θ

Answer 1

Consider the figure :

A perpendicular is drawn from D to the side AB at point E which makes BCDE is a rectangle.

Now in right-angled triangle BCD using Pythagorean Theorem
⇒ BD² = BC² + CD² ...( AB is hypotenuse in ΔABD)

⇒ CD₂ = 13₂ – 12₂ = 25

∴ CD = 5

Since BCDE is rectangle so ED 12 cm, EB = 5 and AE = 14 - 5 = 9 

(i) sin Ø = `"CD"/"BD" = (5)/(13)`

tan θ = `"ED"/"AE" = (12)/(9) = (4)/(3)`

(ii) sec θ = `"AD"/"AE"`

sec θ = `"AD"/(9)`

 AD   = 9 secθ

Or

cosec θ = `"AD"/"ED"`

cosec θ = `"AD"/(12)`

 AD = 12cosec θ