Question

Find sin θ, cos θ and tan (90° - θ).

Answer 1

Given:

BC = 30 units (base)

AC = 34 units (hypotenuse)

∠B = 90°

∠C = θ

Step 1: Find the height (AB)

Using the Pythagoras Theorem:

AB² = AC² − BC²

= 34² − 30²

= 1156 − 900 = 256

⇒ AB = `sqrt256` = 16

AB = 16 (opposite to θ)

BC = 30 (opposite to θ)

AC = 34 (hypotenuse)

Step 2: Find the trigonometric values

sin θ = opposite ÷ hypotenuse

= 16 ÷ 34 = `8/17`

cos θ = adjacent ÷ hypotenuse

= 30 ÷ 34 = `15/17`

tan(90° - θ) = cot(θ) = adjacent ÷ opposite

= 30 ÷ 16 = `15/8`