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Zielflug [23.3K]

2 years ago

11

The area of a rectangular wall of a barn is 140 square feet. Its length is 6 feet longer than twice its width. Find the length a

nd width of the wall of the barn.

1 answer:

timofeeve [1]2 years ago

7 0

$l*w=140$
$l=2w+6)$
$(2w+6)*w=2w ^{2} +6w=140$
$70=w^2+3w$
$70=w(w+3)$
w=7
$l=2(7)+6$
$l=20$

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2 years ago

Read 2 more answers

Help pls im being timed

Nitella [24]

The trigonometric ratios show that the angle FHE is 48.59°.

<h3>RIGHT TRIANGLE</h3>

A triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: $(hypothenuse)^2=(leg_1)^2+(leg_2)^2$ . And the main trigonometric ratios are:

$sin(\alpha) =\frac{opposite \;leg }{hypotenuse} \\ \\ cos(\alpha) =\frac{adjacent\;leg }{hypotenuse} \\ \\ tan(\alpha) =\frac{sin(\alpha )}{cos(\alpha )}= \frac{opposite \;leg }{adjacent\;leg } \\ \\$

It is important to remember that the sum of internal angles for any triangle is 180°.

From the question, it is possible to see 2 right triangles (HGF and FHE).

You can find the hypotenuse of the triangle HGF from the trigonometric ratio: sen Θ

$sin45=\frac{opposite\; leg }{hypotenuse} =\frac{\sqrt8}{hypotenuse}\\ \\ \frac{\sqrt{2} }{2} =\frac{\sqrt{8} }{hypotenuse} \\ \\ \sqrt{2}*hypotenuse=2\sqrt{8} \\ \\ hypotenuse=\frac{2\sqrt{8} }{\sqrt{2}} =2\sqrt{4} =2*2=4$

The hypotenuse of triangle HGF is one of legs for the triangle FHE. The, you can find the angle FHE from the trigonometric ratio: tan β. Thus,

$sin \beta =\frac{opposite\; leg }{adjacent\; leg} =\frac{3}{4}\\ \\ sin \beta=\frac{3}{4}=0.84806\\ \\ arcsin\beta =48.59^{\circ \:}$

Learn more about trigonometric ratios here:

brainly.com/question/11967894

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