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2 years ago

In Rectangle ABCD, m

Mathematics

1 answer:

storchak [24]2 years ago

6 0

Answer:

m∠ACD = 24°

Step-by-step explanation:

Measure of the interior angles of a polygon = $\frac{(n - 2)\times 180}{n}$

Therefore, measure of the interior angles of a rectangle = $\frac{(4 - 2)\times 180}{4}$

= $\frac{360}{4}$

= 90°

m∠BCD = 90°

Since, m∠BCD = m∠BCA + m∠ACD

90° = 66° + m∠ACD

m∠ACD = 90° - 66°

= 24°

Therefore, measure of angles ACD is 24°.

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Step-by-step explanation:

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2 years ago

What is longer 180 seconds or 3 minutes

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3 years ago

Read 2 more answers

The angle of elevation to the top of a water tower from point A on the ground is 19.9°. From point B, 50.0 feet closer to the to

zepelin [54]

Answer:

Answer in terms of a trigonometric function :

$h = \frac{20tan(19.9)}{0.4-tan(19.9)}$

Answer in figures

$h = 190.5 feet$

Step-by-step explanation:

Consider the sketch attached below to better understand the problem.

Let x be the distance between point B and the base of the water tower.

$tan (19.9)=\frac{h}{50+x} ---------------equation 1\\$

$tan (21.8)=\frac{h}{x}----------------equation 2$

From equation 2,

$x =\frac{h}{tan21.8}=\frac{h}{0.4}$

substituting the value of x into equation 1, we get

$tan (19.9)=\frac{h}{50+(\frac{h}{0.4} )}$

$tan 19.9=h\times \frac{0.4}{20+h}$

cross multiplying,

$20\times tan(19.9) +htan(19.9)=0.4h$

$20tan(19.9)= h(0.4-tan(19.9))$

$h= \frac{20tan (19.9)}{0.4-tan (19.9)}$

The height of the tower is $h= \frac{20tan (19.9)}{0.4-tan (19.9)}$ in terms of the trig function "Tan"

The equation can simply be evaluated to get the answer in figures since the angles are given in the question

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3 years ago

A carton measures 3 feet by 2 feet by 2 feet. A machine can fill the carton with packing material in 3 seconds. How long would i

True [87]

1) we calculate the volume of the first carton:
volume=length x width x height
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Therefore:
A machine can fill 12 ft³ in 3 seconds.

2) we calculate the volume of the second carton.
volume=length x width x heigth
volume=4 ft * 5 ft * 6 ft=120 ft³

3) we calculate the time that the machine needs for fill the second carton with packing material by the rule of three.

12 ft³---------------------3 seconds
120 ft³-------------------- x

x=(120 ft³ * 3 seconds) / 12 ft³=30 seconds.

answer: 30 seconds.

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2 years ago

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Answer:

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3 years ago