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azamat
1 year ago
7

The diagonals of a rectangle enclose an angle of measure 78 degree

Mathematics
1 answer:
katrin2010 [14]1 year ago
3 0

The area of the rectangle with a perimeter of 36 cm is determined as: 80.1  cm².

<h3>What is the Area of a Rectangle?</h3>

Area of a rectangle = (length)(width).

<h3>Given the following:</h3>

Angle of measure 78 degree enclosed by the diagonals of the rectangle

Perimeter = 36 cm

To find the area, we need to find the length and width of the rectangle using the trigonometric ratios.

A side of the rectangle = x cm

The other side = (36 - 2x)/2  = (18 - x) cm

Angle of the diagonal base = (180 - 78)/2 = 51°

Apply the tangent ratio to find x:

Tangent ratio is tan ∅ = opposite/adjacent side of a right triangle. We have the following,

∅ = 51°

Opposite side = x cm

Adjacent side = (18 - x) cm

Tan 51°  =  x/(18 - x)

1.235 = x/(18 - x)

1.235(18 - x) = x

22.23 - 1.235x = x

22.23 = x + 1.235x

22.23 = 2.235x

22.23/2.235 = 2.235x/2.235

x = 9.946 cm (one side length)

The other side length = 18 - x = 18 - 9.946 = 8.054 cm

Area of the rectangle = (9.946)(8.054)

Area of the rectangle = 80.1  cm²

Learn more about the area of rectangle on:

brainly.com/question/25292087

#SPJ1

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In a random sample of 1066 U.S. adults, 580 think that the U.S. government
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Step-by-step explanation:

This is a test of 2 population proportions. Let 1 and 2 be the subscript for the adults who think that the U.S. government is doing too little to protect the environment presently and the adults who think that the U.S. government is doing too little to protect the environment 10 years ago. The population proportions would be p1 and p2 respectively.

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For 10 years ago,

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The pooled proportion, pc is

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