Question

In rectangle ABCD shown below, CD = 24 and m angle ABD = 35º. Determine the length of diagonal line BD to the nearest tenth. Show the work that leads to your answer.

Answer 1

Answer:

BD = 29.3

Step-by-step explanation:

Each half of the rectangle is a right triangle.

The diagonal is the hypotenuse of each right triangle.

Let's focus on right triangle ABD

Reference angle = m<ABD = 35°

AB = CD = 24

Adjacent length = AB = 24

Diagonal = Hypotenuse = BD

To find BD, apply CAH:

Cos 35° = Adj/Hyp

Substitute

Cos 35° = 24/BD

BD × Cos 35° = 24

BD = 24/Cos 35°

BD = 29.3 (nearest tenth)