Question

can anyone slice plzz

Answer 1

as tanα = 4/5 

Then opp(O) = 4k units and adj(A) = 5k units.

(as tanα = opp/adj)

Then in Δ By Pythagoras theorem,

H² =O² + A²

H² = (4k)² + (5k)²

H² = 16k² + 25k²

H  = √39k²      ⇒ √39 k units. 

Now,

sinα = opp/hypo    ⇒ 4k/√39k   ⇒ 4/√39

cosα = adj/hypo    ⇒ 5k/√39k   ⇒ 5/√39

Then substituting these values,

= 5 sinα - 3 cosα/5 sinα + 2 cosα

= 5(4/√39) - 3(5/√39)/5(4/√39) + 2(5/√39)

= 20 -15/√39 ÷ 20 + 10/√39

(taking reciprocals)

= 5/√39 × √39/30

(cancelling √39 on numerator and denominator)

= 5/30   ⇒ 1/6

Answer = 1/6

☺ Hope this Helps ☺