Question

From the given figure, find the trigonometric ratios of cosa and tan0​

Answer 1

Answer:

cos α = 4/5

tan θ = 5/12

Step-by-step explanation:

Consider ∆ ADC

By Pythagoras theorem,

   AC² = AD² + DC²

⇒ AC² = 3² + 4²

⇒ AC² = 9 + 16

⇒ AC² = 25

⇒ AC = √25

⇒ AC = 5

For finding cos α

cos α = Adjacent side ÷ Hypotenuse

⇒ cos α = DC ÷ AC

⇒ cos α = 4 ÷ 5

∴ cos α = 4/5

For finding tan θ

θ is in ∆ ABC

tan θ = Opposite Side ÷ Adjacent side

tan θ = AC ÷ AB

⇒ tan θ = 5 ÷ AB

Again By Pythagoras theorem,

BC² = AB² + AC²

⇒ 13² = AB² + 5²

⇒ AB² = 144

⇒ AB = 12

Now, tan θ = 5 ÷ AB

∴ tan θ = 5/12