MATHEMATICS HIGH SCHOOL

In two or more complete sentences, explain the theorem used in solving for the range of possible lengths of the third side, AB of triangle ABC

Answers

Answer 1
Answer:

Answer:


Step-by-step explanation:

In triangle if two sides are known and included angle is known we can use cosine formula as follows:

Say in a triangle, sides a,b are known and also included angle C

Then the third side

c^(2) =a^(2)+b^(2) -2abCos C

Since all values on right side are known, we can find the third side c easily.

Case II:

If alternately two sides and one angle not included is known. i.e we know a,b and either angle A or B.

then to find third side we use sine formula.

(a)/(sinA)=(b)/(sinB) =(c)/(sinC)

Using the above we can find the unknonwn side c easily.
Answer 2
Answer: You can use the Pythagorean Theorem to find the length of the third side AB (Identified as "x" in the figure attached in the problem), which says that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs:
 a² = b²+c²
 As we can see the figure, the triangle does not have an angle of 90°, but it can be divided into two equal parts, leaving two triangles with a right angle. We already have the values of the hypotenuse and a leg in triangle "A" , so we can find the value of the other leg:
 b = √(a²-c²) b = √(10²-4²) b = 9.16
 With these values, we can find the hypotenuse in the triangle "B": x = √b²+c² x = √(9.16)²+(4)² x = 10

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The cosine of an angle is the ratio of the opposite side over the hypotenuse.a. True
b. False

Answers

Answer:

False, The cosine of an angle is the ratio of the opposite side over the hypotenuse.

Let ΔABC is a right angled triangle, ∠C = 90°

Figure is attached.

let ∠B be \theta

Then the trigonometric ratios are the following:

sin\,\theta=(AC)/(AB)

cos\,\theta=(CB)/(AB)

tan\,\theta=(AC)/(CB)

cosec\,\theta=(AB)/(AC)

sec\,\theta=(AB)/(CB)

tan\,\theta=(CB)/(AC)

So, clearly cos\,\theta=(Adjacent)/(Hypotenuse)

Its sin\,\theta=(Opposite)/(Hypotenuse)
It's False.Sine is a trigonometric function of the angle in a right triangle is equal to the ratio of the opposite leg to the angle of the hypotenuse.

For which function is the ordered pair (4, 12) not a solution?y = 3x
y = x + 8
y = 16 - x
y = 8 - x

Answers

It's D since 8 - 4 = 4, not 12.

Answer:

Y=8-x

So the answer is in fact D.

Cuantas horas hay de diferencia entre el meridiano qué pasa por el Perú y si antípoda

Answers

Answer:

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At Factory Y, a worker's wages for a 40-hour week is $200. She is paid 10% of her regular weekly wages for every hour that she works overtime. At the end of a certain week she received $380. Calculate the number of hours of overtime that she worked.

Answers

Answer:

She worked 18 hours of overtime.

Step-by-step explanation:

If she works 40 hours per week and gets $200, subtract $380 - $200 = $180.

If you multiply $180 by 0.1 (which is 10% converted to a decimal), you get 18 which is your final answer.

Which is the area of a circle with a radius of 5 units? (use 3.14 for )?

Answers

Answer:

The area of circle is 78.5 units².

Step-by-step explanation:

Area of the circle is defined by the formula A = π r²

Here r = radius of the circle and value of π = 3.14

Now by putting these values in the formula  we can get area of the circle.

A = (3.14) × 5²

A = 3.14 × 25

A = 78.5 units²

The area of circle is 78.5 units²
The area of a circle is A=πr². 
Since π is about 3.14 we can substitute that into the equation.
So A=3.14×r²
We can substitute the given radius for r.
A= 3.14 × 5²
When a number is squared, or has the two over it, we multiply it by itself. 
5 × 5= 25
A= 3.14 × 25
Simplify this and the area of the circle is about 78.5
A≈78.5
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