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Dmitrij [34]
3 years ago
10

A triangle has side lengths of 20 cm, 99 cm, and 108 cm. Classify it as acute, obtuse, or right.

Mathematics
1 answer:
vagabundo [1.1K]3 years ago
8 0
Okay lets go down the list. It's not right since 20²+99²=10201 √10201=101 and you said a is wrong it's have to be B. obtuse
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Given:
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Area = (height * base) / 2

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245 = (14 * b) / 2
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490 = 14b
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2 years ago
The sum of 5 consecutive integers is 265. What is the fifth number in this sequence?
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Five consecutive integers are:

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A rectangle is 7 feet long by 5 feet wide. If 3 feet are removed from the length of the rectangle, what would be the area, in sq
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A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.8 ft/s,
shusha [124]

Answer:

-0.133 radians/s is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall.

Step-by-step explanation:

Let

x= distance between the wall and ladder

Ф = angle between the ladder and ground

The rate of change is: dx/dt = 0.8 ft/s

We need to find dФ/dt when x = 8 ft/s

From the triangle in the figure we see that:

cos Ф = x/10

=> x = 10 cosФ

Now, the rate of change will be

d(x)/dt = d/dt (10cosФ)

dx/dt = -10 sin Ф dФ/dt

dx/dt = 0.8 (given)

to find dФ/dt

we need to find sin Ф when x = 8

By Pythagoras theorem

(hypotenuse)^2 = (Perpendicular)^2+(base)^2

(10)^2 = (8)^2+ (Perpendicular)^2

100 = 64 +  (Perpendicular)^2

=>  (Perpendicular)^2 = 100-64

(Perpendicular)^2 = 36

Perpendicular = 6

sin Ф = Perpendicular/hypotenuse

sin Ф = 6/10 = 3/5

Putting values in:

dx/dt = -10 sin Ф dФ/dt

0.8 = -10(3/5) dФ/dt

0.8 = -6 dФ/dt

=> dФ/dt = 0.8 / -6

dФ/dt = - 0.133 radians/s

So, -0.133 radians/s is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall.

3 0
3 years ago
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