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Helga [31]
2 years ago
5

Angelica says the tangent is the ratio of the length of the leg opposite angle A ∠ A over the length of the leg adjacent to angl

e A This means B C must have a length of 3 3 units A C must have a length of: 4 4 units. They can find the length of Latex A B using the Pythagorean Theorem and then use it to find the sine and cosine ratios. Graciella says that they cannot find the length of any side of the triangle and, therefore, cannot find the ratios for sine and cosine. Both students have errors in their reasoning. Identify the mistake Angelica made in her reasoning. Provide an example that shows why she is incorrect. Identify the mistake that Graciella made in her reasoning. Explain why she is incorrect. Find the ratios for the sine and cosine of angle A Explain your process.
Mathematics
1 answer:
Tpy6a [65]2 years ago
3 0

Based on the trigonometry ratios and the Pythagorean theorem both of them were incorrect.

Cos A = 4/5; Sin A = 3/5

<h3>What is the Trigonometry Ratios?</h3>

The Trigonometry ratios relates the length of the sides of a right triangles. They are given as:

  • Sine ratio, sin ∅ = opp/hyp
  • Cosine ratio, cos ∅ = adj/hyp
  • Tangent ratio, tan ∅ = opp/adj.

<h3>What is the Pythagroean Theorem?</h3>

If two sides of a right triangle are known the third side can be determined using the Pythagorean theorem, which is given as, c² = a² + b², where and b are legs, and c is the hypotenuse of the right triangle.

1. Given that tan A = 3/4, it is not necessarily true that BC MUST have a length of 3 units, and AC MUST have a length of 4 units, because:

If BC = 9 units and AC = 12 units, the it will give us the same tangent ratio as:

tan A = 9/12 = 3/4.

Therefore, Angelica's mistake is stating that BC MUST be 3 units, and AC MUST be 4 units.

2. Knowing two length of the sides of a right triangle is enough information needed to find the length of the third side using the Pythagorean theorem, so Graceilla is incorrect.

3. Find AC using the Pythagorean theorem:

AB = √(3² + 4²)

AB = 5 units.

Cos A = adj/hyp = AC/AB

Cos A = 4/5

Sin A = opp/hyp = BC/AB

Sin A = 3/5

Learn more about the trigonometry ratios on:

brainly.com/question/10417664

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Please help thank you
Gemiola [76]
Question 1:

This is a 45-45-90 right triangle. If the leg length is x, then the hypotenuse length will be x \sqrt{2}.

The leg length of this 45-45-90 right triangle is 8. Multiply that with the square root of 2. You get 8 \sqrt{2}. Thus, the last choice is your answer.

Question 2:

This triangle can be identified as a 30-60-90 right triangle.
Let's say the smallest leg as a length of x.
Then, the longer leg will have a length of x \sqrt{3}.
Also, the hypotenuse will have a length of 2x

This triangle follows this format, making it a 30-60-90 right triangle. Thus, the angles are 30, 60, and 90.

Hope this helps! :)
5 0
3 years ago
Helpppp meeeee plssss
Diano4ka-milaya [45]
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3 0
3 years ago
in the following diagrams ABD=y,DBC=x,EFH=y, EFG=x and PQS=SQR=x.write the following in terms of x and y ABC
Leokris [45]

Angles are the space between intersecting lines, and they are measured in degrees or radians

The measure of angle ABC is y + x

<h3>How to determine angle ABC</h3>

The given parameters are:

ABD=y,

DBC=x,

EFH=y,

EFG=x

PQS = SQR = x

To determine the measure of angle ABC, we make use of angle ABD and angle DBC

Note that angle ABD and angle DBC have common vertices at points B and D

So, we have:

ABC = ABD + DBC

Substitute known values

ABC = y + x

Hence, the measure of angle ABC is y + x

Read more about angle measures at:

brainly.com/question/17972372

3 0
2 years ago
I need help on 13 and 15 that all
mihalych1998 [28]
<span>Anna learns in her science class that the human eye blinks an average of 4,200,000 times a year. What is this number expressed in scientific notation?</span>
8 0
3 years ago
Solve this equation by completing the square: x2 + 4x – 13 = –8
marishachu [46]

Answer:

x = 1 or x = -5

Step-by-step explanation:

We are given;

  • The quadratic equation, x² + 4x - 13 = -8

We are required to solve the equation using the completing square method.

To do this, we use the following steps;

Step 1: We make sure the coefficient of x² is one

x² + 4x - 13 = -8

Step 2: Combine the like terms (take the constant term to the other side)

x² + 4x - 13 = -8

x² + 4x = -8 + 13

we get

x² + 4x  = 5

Step 3: We add the square of half the coefficient of x on both sides of the equation

Coefficient of x = 4

Half of coefficient of x = 2

Square of half the coefficient of x = 2² (4)

We get;

x² + 4x + (2²)  = 5 + (2²)

Step 4: Put x and 2 under one square and the solve the other side of the equation.

We get

(x + 2)² = 5 + 4

(x + 2)² = 9

Step 5: Get the square root on both sides of the equation;

(x + 2)² = 9

√(x + 2)² = ±√9

(x + 2)= ±3

Therefore;

x+2 = + 3 or x + 2 = -3

Thus, x = 1 or -5

The solution of the equation is x = 1 or x = -5

6 0
3 years ago
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