Can anyone help with this?

What is the perimeter of WXYZ?

Lesechka [4]

Answer:

48

Step-by-step explanation:

If the follows triangle congruence, you look at the two triangles given.

Triangle XYZ is equiangular due to it's 3 congruent angles.

Since Triangle XYZ is equiangular, that means it is also equilateral, meaning each side is congruent.

This means that side XY and Side ZY are equal to XZ and therefore

XY = 11 and ZY = 11.

Then we look at Triangle WXZ. Triangle WXZ has two congruent base angles, meaning it's an isosceles triangle.

By the converse of the isosceles triangle theorem, if 2 angles of a triangle are congruent then the sides opposite those angles are congruent.

This means XZ and WZ are congruent to each other, meaning XZ = WZ.

Since XZ= 11, that means WZ = 11.

Now we have all outside side lengths and we can find the perimeter.

Perimeter = WX + WZ + ZY + XY.

(substitute known values of sides)

11+11+11+15= Perimeter

33+15 = Perimeter

48 = Perimeter

5 0

3 years ago

The ratio of Shauntay's cards to Jessica's cards is 5 to 3. After Shauntay gives Jessica 12 of her cards, both girls have the sa

Zepler [3.9K]

Answer:

They have 48 cards.

Step-by-step explanation:

let s be the number of Shauntay's cards and j be the number of Jessica's cards.

The ratio of Shauntay's cards to Jessica's cards is 5 to 3, then

(1) $\frac{s}{j}$ = $\frac{5}{3}$

After Shauntay gives Jessica 12 of her cards, both girls have the same number of cards, then

(2) s-12 =j+12.

From (2), we get s= j+24. If we put j+24 instead of s in (1) we get:

$\frac{j+24}{j}$ = $\frac{5}{3}$

3×j+24×3 = 5×j From this we get;

2×j=72 and j=36

After Shauntay gives Jessica 12 of her cards, Shauntay and Jessica would have 48 cards.

4 0

3 years ago

Find the Value of Sin A rounded to the nearest hundredth, if necessary.

leonid [27]

Step-by-step explanation:

In trigonometry, the law of sines is an equation that relates the length of the sides of a triangle (any type of triangle) to the sines of its angles. This is expressed mathematically as

$\displaystyle\frac{a}{\sin \alpha} \ = \ \displaystyle\frac{b}{\sin \beta} \ = \ \displaystyle\frac{c}{\sin \gamma}$ ,

where $a$ , $b$ , and $c$ are the lengths of the sides of the triangle and $\alpha$ , $\beta$ , and $\gamma$ are the opposite angles (as shown in the figure below). Likewise, the law is sometimes written as it reciprocals,

$\displaystyle\frac{\sin \alpha}{a} \ = \ \displaystyle\frac{\sin \beta}{b} \ = \ \displaystyle\frac{\sin \gamma}{c}$ .

Therefore,

$\displaystyle\frac{\sin A}{BC} \ = \ \displaystyle\frac{\sin B}{AC} \\ \\ \\ \sin A \ = \ \displaystyle\frac{\sin B \ \times \ BC}{AC} \\ \\ \\\sin A \ = \ \displaystyle\frac{\sin \left(90^{\circ}\right) \ \times \ \sqrt{\left(10\right)^{2} \ - \ \left(\sqrt{78}\right)^{2}}}{10} \\ \\ \\ \sin A \ = \ \dsiplaystyle\frac{\sqrt{22}}{10} \\ \\ \\ \sin A \ = \ 0.47 \ \ \ \ (\text{nearest hundredth})$

Alternatively, you can solve this question using the definition of the trigonometric function sine. For the angle $\theta$ in the figure below,

$\sin \theta \ = \ \displaystyle\frac{\text{opposite}}{\text{hypothenuse}}$ .

Therefore,

$\sin A \ = \ \displaystyle\frac{BC}{AC} \\ \\ \\ \sin A \ = \ \displaystyle\frac{\sqrt{\left(10\right)^{2} \ - \ \left(\sqrt{78}\right)^{2}}}{10} \\ \\ \\ \sin A \ = \ \displaystyle\frac{\sqrt{22}}{10} \\ \\ \\ \sin A \ = \ 0.47 \ \ \ \ (\text{nearest hundredth})$