if in a triangle ABC right angled at B AB =6cm and BC=8cm then find the value of sinA.cosC+cosA.sinC.
Answers
Given : a triangle ABC right angled at B AB =6cm and BC=8cm
To Find : the value of sinA.cosC+cosA.sinC.
Solution:
AB = 6 cm
BC = 8 cm
AC² = AB² + BC²
=>AC² = 6² + 8²
=> AC² = 36 + 64
=> AC² = 100
=> AC = 10
Sin A = BC/AC = 8/10 = 4/5
CosC = BC/AC = 8/10 = 4/5
CosA = AB/AC = 6/10 = 3/5
SinC = AB/AC = 6/10 = 3/5
sinA.cosC+cosA.sinC
=> (4/5)(4/5) + (3/5)(3/5)
= 16/25 + 9/25
= (16 + 9)/25
= 25/25
= 1
sinA.cosC+cosA.sinC. = 1
Another method :
sinA.cosC+cosA.sinC = Sin (A + C)
A + C = 90° as B = 90° and A + B + C = 180°
=> Sin 90° = 1
sinA.cosC+cosA.sinC. = 1
Learn More:
there exist a tower near Shankar's house . The top of the toweer AB ...
brainly.in/question/31295368
3.Pythagoras theorem.Make a right triangle of sides given as3cm ...
brainly.in/question/31635513