10th Grade Cosine law (Nikoleta Simeonova)

Reviewed by Editorial Team

The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.

Learn about Our Editorial Process

| By ACS_Math

ACS_Math

Community Contributor

Quizzes Created: 6 | Total Attempts: 817

| Attempts: 148

Quiz Flashcard

Questions

Feedback

During the Quiz End of Quiz

Difficulty

Easy First Hard First Sequential

Share on Facebook Share on Twitter Share on Whatsapp Share on Pinterest Share on Email Copy to Clipboard Embed on your website

1/10 Questions

Given ABCD - circumscribed quadrilateral. Two of the adjacent sides are 5 cm and 12 cm, they are also perpendicular to each other. Find the other sides if the angle between them is 60 degrees.

About This Quiz

For your "fill in the blanks" answers, please use the following pattern:
_ cm, _ cm
Example:
1 cm, 2 cm

10th Grade Cosine Law (Nikoleta Simeonova) - Quiz

2.

Given an equilateral triangle ABC with a side 3 cm. The equilateral triangle DEF is inscribed in ABC, DE= cm, D lies on AB. Find the lengths of the line segments AD and DB.

Explanation
In an equilateral triangle, all sides are equal. Given that side AB of triangle ABC is 3 cm, and triangle DEF is inscribed in ABC, we can conclude that side DE is also 3 cm. Since D lies on AB, the lengths of line segments AD and DB can be determined by dividing the side AB equally. Therefore, AD and DB are both 1 cm and 2 cm respectively.

Rate this question:
3.

Given a triangle ABC with sides 5 cm and 10 cm. The median to the third side is with 2,5 cm shorter than the third side. Find the third side.
4.

Given a parallelogram ABCD with sides 11 cm and 16 cm. From one of the acute angles a perpendicular is dropped on the shorter diagonal. The length of that perpendicular is cm. Find the longer diagonal of ABCD.

Explanation
In a parallelogram, opposite sides are equal in length. So, if one side is 11 cm, then the opposite side is also 11 cm. The shorter diagonal of the parallelogram is the perpendicular dropped from one of the acute angles to the opposite side. Since the length of this perpendicular is 23 cm, it is equal to the length of the shorter diagonal. Therefore, the longer diagonal of the parallelogram is also 23 cm.

Rate this question:
5.

The following identity is true or false:
- True
- False
Correct Answer

A. False
6.

The following identity is true or false:
- True
- False
Correct Answer

A. False
7.

The following identity is true or false:
- True
- False
Correct Answer

A. True

Explanation

The given question asks whether the following identity is true or false. The correct answer is "True," indicating that the identity is indeed true. However, without knowing the specific identity mentioned in the question, it is not possible to provide a detailed explanation of why it is true.

Rate this question:
8.

Given an equilateral triangle ABC with a side 6 cm. Point M lies on AB, so that the distance between M and the nearest vertex of the triangle is 1 cm. Find the distance between M and the centroid of ABC.
- 6
Correct Answer

A.

Explanation

The distance between M and the centroid of an equilateral triangle is always two-thirds of the distance between M and the nearest vertex. In this case, the distance between M and the nearest vertex is 1 cm, so the distance between M and the centroid is (2/3) * 1 cm = 2/3 cm.

Rate this question:
9.

Given a triangle ABC with sides BC=2 cm, AB=5 cm, AC= cm. Point D lies on AC, so that BD=3 cm. Find CD.
Correct Answer

A.

Explanation

In the given triangle ABC, we are given that BD=3 cm. Since D lies on AC, we can use the property of similar triangles to find CD. By using the similarity property, we can write the proportion: BD/CD = AB/AC. Plugging in the given values, we get 3/CD = 5/(AC-3). Cross-multiplying and simplifying, we get 5CD - 15 = 3AC - 9. Rearranging the equation, we get 5CD - 3AC = 6. Now, we can substitute the value of AC from the given information (AC = BC + CD) and solve the equation to find the value of CD.

Rate this question:
10.

Given a parallelogram ABCD with a perimeter 22 cm. The longer diagonal is 9 cm, the shorter diagonal equals the longer side of ABCD. Find the sides of ABCD.
- 4 cm, 7 cm
- 3 cm, 8 cm
Correct Answer(s)

A. 4 cm, 7 cm
A.

Explanation

Let the longer side of ABCD be x cm. Since the shorter diagonal equals the longer side, the shorter diagonal is also x cm. The perimeter of a parallelogram is equal to the sum of all its sides, so we have 2x + 2(x+9) = 22. Simplifying this equation gives us 4x + 18 = 22, which further simplifies to 4x = 4. Solving for x, we find that x = 1. Therefore, the sides of ABCD are 1 cm and 1+9 = 10 cm. However, this contradicts the given answer choices, so the question may be incomplete or not readable.

Rate this question:

Quiz Review Timeline (Updated): May 27, 2024 +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

Current Version
May 27, 2024

Quiz Edited by
ProProfs Editorial Team
Mar 28, 2013

Quiz Created by
ACS_Math

10th Grade Cosine Law (Nikoleta Simeonova)

Given ABCD - circumscribed quadrilateral. Two of the adjacent sides are 5 cm and 12 cm, they are also perpendicular to each other. Find the other sides if the angle between them is 60 degrees.

Quiz Preview

Given an equilateral triangle ABC with a side 3 cm. The equilateral triangle DEF is inscribed in ABC, DE= cm, D lies on AB. Find the lengths of the line segments AD and DB.

Given a triangle ABC with sides 5 cm and 10 cm. The median to the third side is with 2,5 cm shorter than the third side. Find the third side.

Given a parallelogram ABCD with sides 11 cm and 16 cm. From one of the acute angles a perpendicular is dropped on the shorter diagonal. The length of that perpendicular is cm. Find the longer diagonal of ABCD.

The following identity is true or false:

The following identity is true or false:

The following identity is true or false:

Given an equilateral triangle ABC with a side 6 cm. Point M lies on AB, so that the distance between M and the nearest vertex of the triangle is 1 cm. Find the distance between M and the centroid of ABC.

Given a triangle ABC with sides BC=2 cm, AB=5 cm, AC= cm. Point D lies on AC, so that BD=3 cm. Find CD.

Given a parallelogram ABCD with a perimeter 22 cm. The longer diagonal is 9 cm, the shorter diagonal equals the longer side of ABCD. Find the sides of ABCD.