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sveticcg [70]
3 years ago
7

If a 60-degree angle is bisected and then each new angle is bisected, what is the measure of the smallest angle formed?

Mathematics
1 answer:
Ainat [17]3 years ago
4 0
Bisect 60 to get 2 thirty degree
bisect the 30 to get 4 fifteen degrees answer is 15
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I can’t figure out, can someone please explain how to get the correct answer?
Karolina [17]

Answer:

  a)  CD = 9

  b)  AB = 20

Step-by-step explanation:

<h3>a)</h3>

In this geometry, all of the right triangles are similar. This means The ratio of short side to long side is the same for all of the triangles.

You are given the short and long sides of ΔADB, and the long side of ΔCDA. You are asked for the short side of ΔCDA, so you can write the proportion ...

  CD/AD = AD/BD

  CD/12 = 12/16

  CD = 12(12/16)

  CD = 9

__

<h3>b)</h3>

There are a couple of options for finding AD. One you may be familiar with is the Pythagorean theorem.

  AB² = AD² +DB²

  AB² = 12² +16² = 144 +256 = 400 . . . . fill in known values

  AB = √400 = 20 . . . . . take the square root

__

Alternatively, you can use the same proportional relationship that is described above. Here, we make use of the ratio of the hypotenuse to the long side.

  AB/BD = CB/AB

  AB² = BD·CB = 16·(16+9) = 16·25 . . . . cross multiply; fill in known values

  AB = √(16·25) = 4·5 . . . . . take the square root

  AB = 20

_____

<em>Additional comment</em>

This geometry, where the altitude of a right triangle is drawn, has some interesting properties. We have hinted at them above.

You can write three sets of proportions for this geometry: the ratios of short side and long side; the ratios of short side and hypotenuse; and the ratios of long side and hypotenuse. When you look at the way the sides touching the longest hypotenuse relate to that hypotenuse, you see three similar relations:

  AC = √(CD·CB)

  AD = √(DC·DB)

  AB = √(BD·BC) . . . . . . . . the relation used in part (b) above

This "square root of a product" is called the <em>geometric mean</em>. In effect, the length of a side touching the longest hypotenuse is the geometric mean of the two segments of that hypotenuse that it touches.

7 0
2 years ago
How do you this 3 (g-3)=6
Elenna [48]
3(g-3)=6
3g-9=6
3g=15
g=5
that's the answer

4 0
3 years ago
Read 2 more answers
9dx10=240 pls hurry
vaieri [72.5K]

Answer:

2.6 or \frac{8}{3}

Step-by-step explanation:

9d×10=240

÷10        ÷10

9d =24

÷9      ÷9

2.6 or \frac{8}{3}

8 0
2 years ago
As a summer job, Bart is picking strawberries at his uncle's farm. He can pick 6
avanturin [10]

Answer:

125

Step-by-step explanation:

All the work is in picture attat

5 0
1 year ago
25 pts
baherus [9]

Answer:

$4.42!

Step-by-step explanation:

Just add all the prices together then divide by 2!

$1.10 * 2 + $3.79 + $0.95 * 3 = $8. 84

$8.84 ÷ 2 = $4.42!

5 0
2 years ago
Read 2 more answers
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