All categories

3 years ago

In triangle △ABC, ∠ABC=90°, BH is an altitude. Find the missing lengths. AB=4 and BC=3, Find AH, CH and BH.

Mathematics

1 answer:

IRISSAK [1]3 years ago

3 0

Answer:

AH = 3.2
CH = 1.8
BH = 2.4

Step-by-step explanation:

It can be convenient to compute the length of the hypotenuse of this triangle (AC). The Pythagorean theorem tells you ...

AC^2 = AB^2 + CB^2

AC^2 = 4^2 + 3^2 = 16 + 9 = 25

AC = √25 = 5

The altitude divides ∆ABC into similar triangles ∆AHB and ∆BHC. The scale factor for ∆AHB is ...

scale factor ∆ABC to ∆AHB = AB/AC = 4/5 = 0.8

And the scale factor to ∆BHC is ...

scale factor ∆ABC to ∆BHC = BC/AC = 3/5 = 0.6

Then the side AH is 0.8·AB = 0.8·4 = 3.2

And the side CH is 0.6·BC = 0.6·3 = 1.8

These two side lengths should add to the length AC = 5, and they do.

The remaining side BH can be found from either scale factor:

BH = AB·0.6 = BC·0.8 = 4·0.6 = 3·0.8 = 2.4

_____

The sides of interest are ...

AH = 3.2

CH = 1.8

BH = 2.4

You might be interested in

I need help. I suck at Geometry

Temka [501]

Answer:

Step-by-step explanation:

We can use the Pythagorean theorem to fin x

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

7^2 + 24^2 = x^2

49+ 576 = x^2

625 = x^2

Take the square root of each side

sqrt( 625) = sqrt(x^2)

25 = x

4 0

3 years ago

Read 2 more answers

I need help I been hitting a roadblock for the past hour. Can anyone help me?

snow_lady [41]

Answer:

hhuh

Step-by-step explanation:

7 0

3 years ago

Help please with this question

choli [55]

Answer:

They lose about 2.79% in purchasing power.

Step-by-step explanation:

Whenever you're dealing with purchasing power and inflation, you need to carefully define what the reference is for any changes you might be talking about. Here, we take <em>purchasing power at the beginning of the year</em> as the reference. Since we don't know when the 6% year occurred relative to the year in which the saving balance was $200,000, we choose to deal primarily with percentages, rather than dollar amounts.

Each day, the account value is multiplied by (1 + 0.03/365), so at the end of the year the value is multiplied by about

... (1 +0.03/365)^365 ≈ 1.03045326

Something that had a cost of 1 at the beginning of the year will have a cost of 1.06 at the end of the year. A savings account value of 1 at the beginning of the year would purchase one whole item. At the end of the year, the value of the savings account will purchase ...

... 1.03045326 / 1.06 ≈ 0.9721 . . . items

That is, the loss of purchasing power is about ...

... 1 - 0.9721 = 2.79%

_____

If the account value is $200,000 at the beginning of the year in question, then the purchasing power <em>normalized to what it was at the beginning of the year</em> is now $194,425.14, about $5,574.85 less.

7 0

3 years ago

There were 214 people at a concert. Main floor tickets cost $17 and balcony tickets cost $11 for a total of $2954. How may balco

earnstyle [38]

There is 100 $17 tickets no 114 $11 tickets

6 0

3 years ago

Please help will mark Brainliest

alekssr [168]

Answer:

It i s 6

Step-by-step explanation:

Very six

6 0

3 years ago