How coral polyps form a reef

1 answer:

8 0

Coral reefs begin to form when free-swimming coral larvae attach to submerged rocks or other hard surfaces along the edges of islands or continents. As the corals grow and expand, reefs take on one of three major characteristic structures —fringing, barrier or atoll.

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In ∆ABC the angle bisectors drawn from vertices A and B intersect at point D. Find m∠ADB if: m∠C=γ

mylen [45]

Answer:

∠ADB = γ/2 +90°

Step-by-step explanation:

Here's one way to show the measure of ∠ADB.

∠ADB = 180° - (α + β) . . . . . sum of angles in ΔABD

∠ADB + (2α +β) + γ + (2β +α) = 360° . . . . . sum of angles in DXCY

Substituting for (α + β) in the second equation, we get ...

∠ADB + 3(180° - ∠ADB) + γ = 360°

180° + γ = 2(∠ADB) . . . . . . add 2(∠ADB)-360°

∠ADB = γ/2 + 90° . . . . . . . divide by 2

_____

To find angles CXD and CYD, we observe that these are exterior angles to triangles AXB and AYB, respectively. As such, those angles are equal to the sum of the remote interior angles, taking into account that AY and BX are angle bisectors.

5 0

3 years ago

Need help finding the area of the shaded region. Round to the nearest tenth. Need help ASAP

Sergio [31]

Answer: 294.4 m²

Step-by-step explanation:

Separate the shaded region into two parts:

The section containing the central angle of 230° (360° - 130°)
The triangle with sides 11.1, 11.1 & 20.12 (use Law of Cosines)

$1.\ Area(A)=\pi\ r^2\ \bigg(\dfrac{\theta}{360}\bigg)\\\\\\.\qquad \qquad =\pi(11.1)^2\bigg(\dfrac{230}{360}\bigg)\\\\\\.\qquad \qquad =247.3$

$2.\ \text{Use Law of cosines to find the length of the third side.}\\\text{ Then use Heron's formula to find the Area of the triangle.}\\\\s=\dfrac{11.1+11.1+20.12}{2}=21.16\\\\\\A=\sqrt{s(s-a)(s-b)(s-c)}\\\\.\ =\sqrt{21.16(21.16-11.1)(21.16-11.1)(21.16-20.12)}\\\\.\ =\sqrt{2227}\\\\.\ =47.1$