Question

Use triangle XYZ to answer questions 1-3

Answer 1

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.

RIGHT TRIANGLE

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