Mathematics, 20.12.2019 00:31 chris199825

Solve the given triangles by finding the missing angle and other side lengths.

Answers: 3

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Answer from: reecedstceklein

a ≈ 27.65; B = 28°; c ≈ 19.17a ≈ 163.30; B = 120°; c ≈ 59.77A = 13°; b ≈ 0.3874; c ≈ 1.3737

Step-by-step explanation:

As long as you're seeking outside help, the use of a suitable tool is appropriate. Many graphing calculators, apps, and web sites are available for solving triangles.

Here, you're given two angles and a side. The third angle is the difference from 180° of the sum of the other two. For example, in the first problem, ...

B = 180° -A -C = 28°

The missing sides are found using the law of sines. Since you are given a side, use that as the reference, and its opposite angle as the reference angle. Then you have ...

side = sin(opposite angle)×((reference side)/sin(reference angle))

Note that the factor in italics remains the same for both remaining sides.

In the first problem, this becomes ...

a = sin(112°)·14/sin(28°) ≈ 27.65

c = sin(40°)·14/sin(28°) ≈ 19.17

The remaining problems are worked in similar fashion.

_____

Comment on triangle solutions

These are straightforward because you're given two angles. If you're given two sides and an angle, the solution method varies depending on which angle you're given (opposite the long side, the short side, or the unknown side). In the last case, the law of cosines is involved. In the second case, there are likely two solutions. Once you have two angles, you can proceed as above.

Solve the given triangles by finding the missing angle and other side lengths.

Answer from: santosbeti90

The answer to your question is below

Step-by-step explanation:

First picture

1.- Find B

The sum of the internal angles in a triangle equals 180°

40° + 112° + B = 180°

B = 180 - 40 - 112

B = 28°

2.- Find c using law of sines

$\frac{c}{sin C} = \frac{b}{sin B}$

$c = \frac{b sinC}{sin B}$

$c = \frac{14 sin 40}{sin 28}$

c = 19.2

2.- Find a using law of sines

$\frac{a}{sin A} = \frac{b}{sin B}$

$\frac{a}{sin 112} = \frac{14}{sin 28}$

$a = \frac{14 sin 112}{sin 28}$

a = 27.65

Second picture

1.- Find B

The sum of the internal angles in a triangle equals 180

A + B + C = 180

B = 180 - 15 - 45

B = 120°

2.- Find a

$\frac{a}{sin45} = \frac{200}{sin 120}$

$a = \frac{200 sin 45}{sin 120}$

a = 163.3

3.- Find c

$\frac{c}{sin 15} = \frac{163.3}{sin 45}$

$c = \frac{163.3 sin 15}{sin 45}$

c = 59.8

Picture 3

1.- Find A

The sum of the internal angles in a triangle equals 180°

A + B + C = 180°

A = 180 - 162 - 5

A = 13°

2.- Find b

$\frac{b}{sin 5} = \frac{1}{sin 13}$

$b = \frac{1 sin 5}{sin 13}$

b = 0.39

3.- Find c

$\frac{c}{sin 162} = \frac{1}{sin 13}$

$c = \frac{1 sin 162}{sin 13}$

c = 1.37

Answer from: Quest

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !

Answer from: Quest

(0,,,0)

step-by-step explanation:

the table of x and y values is shown in the attached pic(part of question)

we have to decide according that graph

given points are (0, 0) (–1, 0), (2, 0)

when we graph these points on graph they show an increasing line as shown in the attached pic

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