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3 years ago

Name a pair of adjacent complementary angles

Mathematics

1 answer:

Art [367]3 years ago

6 0

Step-by-step explanation:

$\angle \: ABD = 30 \degree \\ and \\ \angle \:CBD = 60 \degree \\ are \: a \: pair \: of \: adjacent \: complementary \: \\ angles.$

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A circle is inscribed in an equilateral triangle. A point in the figure is selected at random. Find the probability that the poi

liubo4ka [24]

Answer:

The correct answer is first option 60%

Step-by-step explanation:

The radius of a circle is inscribed in an equilateral triangle with side a = a/2√3

To find the area of equilateral triangle

Here side be 'a'

Area of equilateral = √3a²/4

To find the area of circle

Here radius = a/2√3

Area = πr²

= π(a/2√3)

= 3.14a²/12

To find the probability

probability = area of circle/area of triangle

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= 3.14/3√3

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The correct answer is first option 60%

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3 years ago

An airplane flies due north from ikeja airport for 500km.It then flies on a bearing of 060 from a further distance of 300km befo

Nata [24]

Answer:

482 km

63.94 degrees

Step-by-step explanation:

to solve this question we will use the cosine rule. For starters, draw your diagram. From point A, up north is 500km and 060 from there, another 300. If you join the point from the road junction back to the starting point, yoou have a triangle.

Cosine rule states that

C = $\sqrt{A^{2} + B^{2} -2AB cos(c) }$

where both A and B are the given distances, 500 and 300 respectively, C is the 3rd distance we're looking for and c is the given angle, 060

solving now, we have

C = $\sqrt{500^{2} + 300^{2} -2 * 500 * 300 cos(60) }$

C = $\sqrt{250000 + 90000 - [215000 cos(60) }]$

C = $\sqrt{340000 - [215000 * 0.5 }]$

C = $\sqrt{340000 - [107500 }]$

C = $\sqrt{232500}$

C = 482 km

The bearing can be gotten by using the Sine Rule.

$\frac{sina}{A}$ = $\frac{sinc}{C}$

sina/500 = sin60/482

482 sina = 500 sin60

sina = $\frac{500 sin60}{482}$

sina = 0.8983

a = sin^-1(0.8983)

a = 63.94 degrees

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3 years ago