Mathematics, 26.07.2019 06:30 izzyisawesome5232

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

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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

Answer from: Osorio5116

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.

$\frac{a}{sinA}=\frac{b}{sinB} =\frac{c}{sinC}$

Using the above we can find the unknonwn side c easily.

Answer from: Quest

a 4/6 = 9/12 not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional. if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional

b 2/3 = 12/18

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

Answer from: Quest

8/k

step-by-step explanation:

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In two or more complete sentences, explain the theorem used in solving for the range of possible len...

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