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kipiarov [429]
2 years ago
14

My friend needed help with this and I found the height through the theorem but can't figure out how to get the base of the overa

ll triangle

Mathematics
1 answer:
Aleksandr-060686 [28]2 years ago
6 0

You found CD from the Pythagorean theorem to be ...

... CD = √(5² -2²) = √21

Since triangle ADC ~ triangle ACB, the ratios of corresponding sides are the same:

... AC/AD = AB/AC

... AB = AC²/AD

... AB = 5²/2 = 12.5 . . . . . . . the base of the overall triangle

_____

Then the area (A) is ...

... A = (1/2)bh

... A = (1/2)(12.5)(√21) ≈ 28.64 square units

_____

As you see here, the altitude of a right triangle divides it into three similar triangles. From smallest to largest, they are ...

... ADC ~ CDB ~ ACB

You can figure this using AAA similarity, since the smallest and largest triangles listed above share an acute angle vertex (∠A). That, together with the right angle, means all angles are congruent. After that, then you know ∠ACD ≅ ∠CBD, so you can show the middle sized triangle is similar to the other two.

You might be interested in
What are the answers to these angle questions?​
mafiozo [28]

Step-by-step explanation:

Firstly, we have to find m∠J.

Since all the angles of a Δ equal 180°, angles J, L, and K should have a sum of 180°.

So,

m∠J + m∠L + m∠K = 180°

The diagram shows us that ∠L = 49° and ∠K = 90°, so we plug in those numbers in the equation.

m∠J + 49° + 90° = 180°

Then we simplify

m∠J + 139° = 180°

Subtract 139° to both sides

∠J = 41

Now the other angles.

Since ΔJKL ~ ΔRST, then ∠J ≅ ∠R, ∠K ≅ ∠S, and ∠L ≅ ∠T

Meaning, m∠J = m∠R, m∠K = m∠S, and m∠L = m∠T

Since we know m∠J = 41°, m∠K = 90°, and m∠L = 49° we could plug those in so...

41° = m∠R , 90° = m∠S , and 49° = m∠T

4 0
3 years ago
I need help pleasssss
Yakvenalex [24]

Answer:

  3)  16.2

Step-by-step explanation:

The supplement to the 115° angle on the right is 65°, the same as the angle at upper left. The vertical angles at C are the same measure, so this tells you that the two triangles FCB and ACD are similar by the AA similarity postulate. That being the case, corresponding sides are proportional:

  CB/CD = CF/CA

  CB = CD·CF/CA = 7.2·21.6/9.6

  CB = 16.2

_____

When given two "point-to-point" triangles like this, quite often there is some sort of similarity relationship involved. First, you need to figure out what it is; then you need to make use of it as needed to answer the question being asked.

4 0
3 years ago
Pls help pls help plsss
uranmaximum [27]

Answer: I'm not sure but there's some explanation..

Step-by-step explanation:

K=11

T=20

Symbol I C

Hope this helps!

*You also need a pic

7 0
2 years ago
HURRY NEED HELP NOW 42 POINTS NEED 1 PARAGRAPH FOR EACH QUESTION there are 2 photos I put up and that where the questions are.
Shtirlitz [24]
1. All you have to do to find the area of the figure. IS first find the area of the rectangle. This is easy because all you have to do is base times height. 

22 x 17 =  374

Now to find the area of the triangle all you have to do is  do base times height like a rectangle, but then divide it by 2 afterwords.
19 x 12 = 228 ÷ 2  = 114.

Now add the two area's together:

374 + 114 = 488.

Just do the same with the one below, I've altered the pic a bit to make it easier. 



4 0
3 years ago
Where does the graph of the line y = x − 2 intersect the x-axis
arsen [322]

(0,2) is your answer

Explanation

5 0
2 years ago
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