A rectangular lot is 80 x 290 ft. Find the length of the diagonal and the angle it makes with the longest side.

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which angle? the opposite of the hypotenuse (diagonal line) ?
^no. since it's a rectangle, obviously the opposite angle of the hypotenuse in 90 degrees.
**is 90 degrees...
yeah.. so you're looking for other angles?
The inquirer, Mhaiko, is looking for the angle along the longest side (between diagonal and longest side which is 290 ft. :-)

Answers

2016-03-13T14:39:50+08:00
To find the diagonal line
we can use Pythagorean theorem 
c^2= a^2+b^2
c=(a^2+b^2)^1/2
c=(80^2 + 290^2)^1/2
c=300.8322 ft.

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  • Brainly User
2016-03-13T15:43:05+08:00
Diagonal of the square/rectangle = hypotenuse

Use Pythagorean Theorem to solve for the diagonal:

Diagonal =  \sqrt{(80) ^{2}+(290) ^{2}  }

Diagonal =  \sqrt{6,400 + 84,100}

Diagonal =  \sqrt{90,500}

Diagonal ≈ 300.8321 ft or 301 ft.

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Angle the diagonal makes with the longest side:

tan θ = opposite side / adjacent side

tan θ = 80 ft. / 290 ft.

tan ⁻¹ θ = 0.27586

θ ≈ 15.42 °  or 15°


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