MATHEMATICS HIGH SCHOOL

I am a little confused: One method you can use to determine whether a triangle is a right triangle, given three side lengths, is to apply the converse of the Pythagorean Theorem. Alternately, you can use trigonometric ratios. Show that the triangle in the diagram is a right triangle by using trigonometric ratios. ( Be sure to show all work/and or reasoning.

Answers

Answer 1
Answer:

Answer with explanation:

The triangle in the Diagram Described has following measurement:

 Longest Side = 65 units

One side which can be either Perpendicular or base = 63 units

And , other side which can be also, either Perpendicular or base = 16 units

We can prove that the triangle described is right triangle by two ways.

1. Using Converse of Pythagorean Theorem

Square of Longest side = Sum of Squares of other two sides-----(1)

So, Square of Longest Side =  65²=4225

Sum of Square of other two sides = 16² + 63²

                                        = 256 + 3969

                                        =  4225

Statement (1), is valid.

So,Triangle is right angled triangle, right angled at A.

2. using Trigonometric Ratios

Suppose the triangle is right Angled at A.

In Right triangle B AC

tan B=\frac{\text{Perpendicular}}{\text{Base}}\n\ntan B=(16)/(63)\n\ntan C=(63)/(16)\n\n tan(B +C)=(tan B + tan C)/(1-tan B * tanC)\n\ntan (B +C)=((16)/(63)+(63)/(16))/(1-(16)/(63)* (63)/(16))\n\ntan (B +C)=\frac{\text{Any rational number}}{0}\n\ntan (B +C)=\infty\n\nB +C=90^(\circ)\n\n \text{Using the trigonometric Identity},tan(A+B)=(tan A +tan B)/(1-tan A*tan B)

B +C =90°

Also,→ ∠A + ∠B + ∠C=180°≡ (Angle sum property of triangle)

→∠A +90°=180°

→∠A=180° -90°

→∠A=90°

So, triangle is right Angled triangle , Right angled at A.

Hence ,proved.
Answer 2
Answer: Trigonometric ratios are sine, cosine, and tangent (opposite side over hypotenuse, adjacent side over hypotenuse, and opposite side over adjacent side, respectively); if you wanted to prove that one of the angles of the triangle is 90º, then the cosine of that angle would be 0, the sine would be 1, and the tangent would be undefined. 

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How do I write 4(3x+2)-9 in written form?

Answers

Step-by-step explanation:

4 times 3x+2 subtracted by9

hope it helps

stay safe healthy and happy.

Answer:

12x-1

Step-by-step explanation:

First, you would have to distribute. Would mean to multiply the 4 with every number in the parenthesis.

4(3x+2)-9

12x+8-9

Now combine like terms

8-9 = -1

The answer is 12x-1

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median = 160
mode = 180
Which value gives Turner's game average?

Answers

Answer:

The mean gives Turner’s game average.

Step-by-step explanation:

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Solve the inequality 6x − 8 > 4x + 26.x < 9

x < 17

x > 9

x > 17

Answers

Answer:

The last option is the correct answer.

Step-by-step explanation:

The given inequality is :

6x-8>4x+26

Pairing the like terms together we have :

6x-4x>26+8

=> 2x>34

Now we will divide both sides by 2;

=> x>17

Thus, the answer is x>17.

The last option is the correct answer.
Hello,
Answer D (x>17)

6x-8>4x+26
==>6x-4x>26+8
==>2x>34
==>x>17

Plzzzz help me with this question ❓​

Answers

Answer:

i think u should first givr her discount by doing 20/100×3500=700 and than he will get 5 percent profit than here

3500-700=2800

now for 5 % profit

5/100*2800=140

hence

20% discount=700

5% profit =140

it might be wrong but here u go

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Answers

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