Question

In ΔABC, ∠A = 0, ∠B = 90° and ∠C = `phi`. If BC = x and AC = (x + 2), find the values of

1. `(sqrt(x + 1)) cot phi`,
2. `(sqrt(x^3 + x^2)) tan θ`,
3. cos θ.

Answer 1

i. `cot phi = (BC)/(AB)`

= `x/(2sqrt(x + 1))`

⇒ `(sqrt(x + 1)) cot phi = x/2`

ii. `tan θ = (BC)/(AB)`

= `x/(2sqrt(x + 1))`

= `x/(2sqrt(x + 1)) xx (sqrt(x^2))/(sqrt(x^2))`

= `(x^2)/(2sqrt(x^3 + x^2))`

⇒ `(sqrt(x^3 + x^2)) tan θ = x^2/2`

iii. `cos θ = (AB)/(AC)`

= `(2sqrt(x + 1))/((x + 2))`