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pochemuha
2 years ago
9

Use triangle XYZ to answer questions 1-3

Mathematics
1 answer:
andriy [413]2 years ago
5 0

For the triangle XYZ, the answers are:1)XY=8\sqrt{3}; 2)Exact Area of triangle XYZ= 32\sqrt{3} ft and 3) Area of triangle XYZ = 55.4 ft.

<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: (hypotenuse)^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{opposite \;leg}{adjacent\;leg}

  1. Finding the segment XY.

cos (30 )=\frac{adjacent\;leg}{hypotenuse} \\ \\ \frac{\sqrt{3} }{2} =\frac{XY}{16}  \\ \\ 2XY=16\sqrt{3} \\ \\ XY=8\sqrt{3}\;ft

    2.Finding the exact area of triangle XYZ

The area of a right triangle is equal to  \frac{1}{2}  * base *height. In this exercise the base is equal to 8\sqrt{3}. For finding the height, you should apply the trigonometric ratio for sin.

sin (30 )=\frac{opposite\;leg}{hypotenuse} \\ \\ \frac{{1} }{2} =\frac{XZ}{16}  \\ \\ 2XZ=16\\ \\ XZ=8\;ft

Therefore, the area will be:

\frac{1}{2}  * base *height\\ \\ \frac{1}{2}  * 8\sqrt{3} *8=32\sqrt{3} ft

    3.Finding the area of triangle XYZ  to the nearest tenth of a square ft

Knowing that \sqrt{3}= 1.73205\dots, the solution will be:

\frac{1}{2}  * base *height\\ \\ \frac{1}{2}  * 8\sqrt{3} *8=32\sqrt{3} =32*1.73205=55.4 ft

Learn more about trigonometric ratios here:

brainly.com/question/11967894

#SPJ1

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