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2 years ago

A doghouse is to be built in the shape of a right trapezoid, as shown below. What is the area of the doghouse?

Mathematics

1 answer:

nadya68 [22]2 years ago

5 0

Answer:

66.5 square feet

Step-by-step explanation:

We have to find the area of the doghouse which is in the shape of right trapezoid . that is, Substitute the values, we get, Hence, Area of of the doghouse which is in the shape of right trapezoid is 66.5 square feet.

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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

Write the final answer in simplest radical form

Annette [7]

Answer:

8 $\sqrt{2}$

Step-by-step explanation:

2^(0.5+3) = 2^3.5 = 8√2

6 0

3 years ago

Christina put 15 vegetables on her tray if 1/5 of the vegetables were carrots how many carrots were on the train make a drawing

LiRa [457]

The answer I she had 3 carrots, this I how you solve it

15* 1/5

I do not know how to upload the drawing so sorry about that!

6 0

3 years ago

Alyssa is 1/4 Tammy's height . If Alyssa is 1 1/2 feet tall how tall is Tammy?

denpristay [2]

Your answer would be 6 ft

you already know that Alyssa is 1 1/2 feet tall which is 1/4 of tammy's height.
so you will take 1 1/2 x 4 (the number of 1/4's needed to get a whole number) = 6 feet

3 0

3 years ago

Andrew was working on a project for Science class. He began working on the project at 10:32 a.m. When he finally

Amanda [17]

Answer:

3 hours 43 minutes

3 0

3 years ago

Read 2 more answers