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3 years ago

Find X, round your answer to the nearest tenth of a degree.

Mathematics

2 answers:

murzikaleks [220]3 years ago

6 0

Answer:

Step-by-step explanation:

$\text{Use sine}=\dfrac{opposite}{hypotenuse}\\\\\text{We have}\ opposite=7,\ hypotenuse=12.\\\\\text{Substitute:}\\\\\sin x=\dfrac{7}{12}\approx0.5833\\\\x\approx35.7^o\\\\/look\ at\ the\ table\ in\ the\ attachment/$

Svet_ta [14]3 years ago

3 0

Answer: X = 35.7° (approximately)

Step-by-step explanation: What we have here is a right angled triangle with two sides given. That means we can apply trigonometrical ratios to calculate any of the angles as well as the unknown side of the triangle.

The unknown angle, X shall be the reference angle in this particular question. The side that lies between the right angle and the reference angle is the adjacent, while the one facing the reference angle is the opposite. So we have the hypotenuse already, that is, the longest side, (or the side facing the right angle).

Since we have been given the opposite side (7 units) and the hypotenuse (12 units) we can conveniently apply the sine ratio, which is

Sin X = opposite/hypotenuse

Sin X = 7/12

Sin X = 0.5833

By checking with your table of values, or by using your calculator, we can now find the value of 0.5833

X = 35.65

Rounded off to the nearest tenth of a degree,

X = 35.7°

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A decorative window is made up of a rectangle with semicircles at either end. The ratio of AD to AB is 3:2 and AB is 30 inches.

scZoUnD [109]

Answer: The required ratio will be

$84:1034$

Step-by-step explanation:

Since we have given that

Ratio of AD to AB is 3:2

Length of AB = 30 inches

So, it becomes

$2x=30\\\\x=\frac{30}{2}=15\ inches$

So, Length of AD becomes

$3x=3\times 15=45\ inches$

Now, at either end , there is a semicircle.

Radius of semicircle along AB is given by

$\frac{30}{2}=15\ inches$

So, Area of semicircle along AB and CD is given by

$2\times \frac{\pi r^2}{2}\\\\=\frac{22}{7}\times 15\times 15\\\\=\frac{4950}{7}\ in^2$

Radius of semicircle along AD is given by

$\frac{45}{2}=22.5\ inches$

Area of semicircle along AD and BC is given by

$2\times \frac{1}{2}\pi r^2\\\\=\frac{22}{7}\times \frac{45}{2}\times \frac{45}{2}\\\\=\frac{445500}{28}\ in^2$

And the combined area of the semicircles is given by

$\frac{4950}{7}+\frac{445500}{28}\\\\=\frac{465300}{28}\ in^2$

Area of rectangle is given by

$Length\times width\\\\=AD\times AB\\\\=45\times 30\\\\=1350\ in^2$

Hence, Ratio of the area of the rectangle to the combined area of the semicircles is given by

$1350:\frac{465300}{28}\\\\=1350\times 28:465300\\\\=37800:465300\\\\=84:1034$

Hence, the required ratio will be

$84:1034$

8 0

2 years ago

A triangle is cut from a piece of fabric. The triangle has a height of 8 inches in an area of 120 in.². What is the length of th

andreyandreev [35.5K]

Answer: 30 inches

Step-by-step explanation:

Given:

ABC-tringle

BH= 8 in - height

S= 120 in^2

AC-?

Solution:

S=1/2ab

120in=1/2a*8in

120=4a

4a=120

a=30 in

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3 years ago

2. What is the total surface area of the figure below 5.2 cm 6 cm 9 cm 6 cm 6 cm

babunello [35]

Answer:

Step-by-step explanation:

Area = 5.2 x 6 + 3 x 6 x 9

= 31.2 + 162

= <u>193.2 cm²</u>

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2 years ago

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scZoUnD [109]

answer: (175+125)÷3

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2 years ago

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r-ruslan [8.4K]

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3 years ago

Find X, round your answer to the nearest tenth of a degree.​

Find X, round your answer to the nearest tenth of a degree.