A wire 18 cm long is cut into two pieces. The longer piece is 6 cm longer than the shorter piece.

In Triangle XYZ, measure of angle X = 49° , XY = 18°, and

marissa [1.9K]

Answer:

There are two choices for angle Y: $Y \approx 54.987^{\circ}$ for $XZ \approx 15.193$ , $Y \approx 27.008^{\circ}$ for $XZ \approx 8.424$ .

Step-by-step explanation:

There are mistakes in the statement, correct form is now described:

<em>In triangle XYZ, measure of angle X = 49°, XY = 18 and YZ = 14. Find the measure of angle Y:</em>

The line segment XY is opposite to angle Z and the line segment YZ is opposite to angle X. We can determine the length of the line segment XZ by the Law of Cosine:

$YZ^{2} = XZ^{2} + XY^{2} -2\cdot XY\cdot XZ \cdot \cos X$ (1)

If we know that $X = 49^{\circ}$ , $XY = 18$ and $YZ = 14$ , then we have the following second order polynomial:

$14^{2} = XZ^{2} + 18^{2} - 2\cdot (18)\cdot XZ\cdot \cos 49^{\circ}$

$XZ^{2}-23.618\cdot XZ +128 = 0$ (2)

By the Quadratic Formula we have the following result:

$XZ \approx 15.193\,\lor\,XZ \approx 8.424$

There are two possible triangles, we can determine the value of angle Y for each by the Law of Cosine again:

$XZ^{2} = XY^{2} + YZ^{2} - 2\cdot XY \cdot YZ \cdot \cos Y$

$\cos Y = \frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ}$

$Y = \cos ^{-1}\left(\frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ} \right)$

1) $XZ \approx 15.193$

$Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-15.193^{2}}{2\cdot (18)\cdot (14)} \right]$

$Y \approx 54.987^{\circ}$

2) $XZ \approx 8.424$

$Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-8.424^{2}}{2\cdot (18)\cdot (14)} \right]$

$Y \approx 27.008^{\circ}$

There are two choices for angle Y: $Y \approx 54.987^{\circ}$ for $XZ \approx 15.193$ , $Y \approx 27.008^{\circ}$ for $XZ \approx 8.424$ .

6 0

3 years ago

What name best describes a pencil a line segment or parallel lies or a point or a ray

Yuliya22 [10]

The answer would be line segment.

5 0

3 years ago

The three angle measures in a triangle are congruent. The angles are equiangular! What is the measurement of one of the angles?

gregori [183]

Answer:

60 degrees per angle.

Step-by-step explanation: a triangle has a total of 180 degrees, and the number of sides determine the number of angles it has. in this case, it's an equilateral triangle. 180/3 = 60. all triangles have 3 sides if you didn't know that ;)

4 0

2 years ago

3.42

taurus [48]

Answer:

105

Step-by-step explanation:

7 0

3 years ago

A local pizza shop has a membership program for frequent buyers. The membership costs $15 per month and members get a discounted

MrMuchimi

Answer:

$34

$26.5

Step-by-step explanation:

Membership cost per month = $25

Price of a slice of pizza for members= $1.50

How much would Aaliyah have

to pay the pizza shop if she bought 6 slices of pizza this month

Total cost of Aaliyah on 6 slices of pizza = membership cost per month + prices of 6 discounted pizza

= $25 + $1.50(6)

= $25 + $9

= $34

What would be the

monthly cost for a slices of pizza

Monthly cost of Aaliyah a slices of pizza = membership cost per month + price of 1 discounted pizza

= $25 + $1.5

= $26.5

7 0

3 years ago