# In triangle ABC, angle C is 90, AC is 15, cosine of angle B is √7 / 4. Find AB

Knowing the cosine of the angle ABC, we determine the sine of this angle.

Sin2ABC = 1 – Cos2ABC = 1 – (√7 / 4) 2 = 1 – 7/16 = 9/16.

SinABC = 3/4.

Through the sine of the angle and the opposite leg, we determine the length of the hypotenuse AB.

SinABS = AC / AB.

AB = AC / SinABC = 15 / (3/4) = 15 * 4/3 = 20 cm.

Answer: The length of the hypotenuse AB is 20 cm.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
The text passage contains a mathematical problem involving a right-angled triangle and trigonometric functions, followed by a detailed solution and the final answer. It also includes a general statement about the importance of education.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# In triangle ABC, angle C is 90, AC is 15, cosine of angle B is √7 / 4. Find AB

Knowing the cosine of the angle ABC, we determine the sine of this angle.

Sin2ABC = 1 – Cos2ABC = 1 – (√7 / 4) 2 = 1 – 7/16 = 9/16.

SinABC = 3/4.

Through the sine of the angle and the opposite leg, we determine the length of the hypotenuse AB.

SinABS = AC / AB.

AB = AC / SinABC = 15 / (3/4) = 15 * 4/3 = 20 cm.

Answer: The length of the hypotenuse AB is 20 cm.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
user
The text passage contains a mathematical problem involving a right-angled triangle and trigonometric functions, followed by a detailed solution and the final answer. It also includes a general statement about the importance of education.

TYPE: SINGLE_QUESTION_WITH_ANSWER