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Find the length of a diagonal AB in the rectangular prism

Find the length of a diagonal AB in the rectangular prism-example-1
User Lukesrw
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1 Answer

4 votes

Hi there!


\large\boxed{AB = 32.60 in}

Find the length of AB by finding the length of its base:

We can use sine to solve for the length of the Hypotenuse of the triangle located in the base:

sin = O / H

sin 50° = 24 / H

h * sin 50° = 24 ----> h = 24 / (sin 50°)

h ≈ 31.33 in

Use the Pythagorean Theorem to solve for the length of the diagonal since we have solved for the base of the triangle:

c² = a² + b²

c² = 31.33² + 9²

c² = 1062.57

c ≈ 32.60 in

AB = 32.60 in