Question

Parallelogram ABCD is a rhombus. Side BC = 5cm and segment AO = 3.8cm

What is the measure of angle d₁°?
What is the tangent ratio of angle c₂?

Answer 1

Let's call angle d₁ "θ". To find θ, we can use the Pythagorean theorem. The segment AO is the hypotenuse of a right triangle with sides BC/2 and AC/2 (since the rhombus is a parallelogram, opposite sides are equal).

AC/2 = (BC/2) / tan(θ)

So:

tan(θ) = AC/2 / (BC/2)

Plugging in the values we have:

tan(θ) = 3.8 / (5/2) = 3.8 / 2.5 = 1.52

Therefore,

θ = tan^(-1)(1.52) = 55.23°

The tangent ratio of angle c₂ is simply the tangent of the angle:

tan(c₂) = tan(90° - θ) = tan(90° - 55.23°) = tan(34.77°) = 1.52

So the tangent ratio of angle c₂ is 1.52.

Explanation: