Question

From the given figure, prove that θ + ∅ = 90°. Also prove that there are two other right angled triangles. Find sin α, cos β and tan ∅

Answer 1

In the ΔABC,

AB = 9 + 16 = 25

AC = 15, BC = 20

AB² = 25²

= 625  ...(1)

AC² + BC² = 15² + 20²

= 225 + 400

= 625  ...(2)

From (1) and (2) we get

AB² = AC² + BC²

ABC is a right angle triangle at C ...(Pythagoras theorem)

∴ ∠C = 90°

θ + ∅ = 90°

Also ADC is a right angle triangle ∠ADC = 90° ...(Given)

BDC is also a right angle triangle ∠BDC = 90° ...(since ADB is a straight line sum of the two angle is 180°)

From the given diagram

sin α = `"DC"/"AC" = 12/15 = 4/5`

cos β = `"BD"/"BC" = 16/20 = 4/5`

tan Φ = `"BD"/"CD" = 16/12 = 4/3`