Question

В треугольнике ABC угол C = 90 градусов, sin A = 9 корней из 181 / корень из 181. Найти: tg A. Посмотрел уже кучу видеоуроков, так ничего и не понял.

Answer 1

TgA=sinA/cosA
sin^2A+cos^2A=1
cos^2(A)=1-sin^2(A)=1-(9/√181)^2=
(181-81)/181=100/181
cosA=√100/181=10/√181
tgA=sinA:cosA=9/√181:10/√181=9/10
tgA=9/10

Answer 2

Task: Find the value of tg(A) in a triangle ABC, where angle C is 90 degrees and sin(A) is equal to 9√181/√181.

To find the value of tg(A), we need to use the given information about the triangle ABC. Let's break down the problem step by step:

1. Given information: - Angle C = 90 degrees - sin(A) = 9√181/√181

2. Relationship between sin and tg: - We know that sin(A) = opposite/hypotenuse and tg(A) = opposite/adjacent in a right triangle. - Since angle C is 90 degrees, we can use trigonometric ratios to find the values of sin(A) and tg(A).

3. Finding the values: - From the given information, we have sin(A) = 9√181/√181. - We can simplify this expression by canceling out the common factor of √181: - sin(A) = 9√181/√181 = 9/1 = 9. - Therefore, sin(A) = 9.

4. Using the relationship between sin and tg: - We can use the relationship sin(A) = opposite/hypotenuse and tg(A) = opposite/adjacent to find the value of tg(A). - In a right triangle, the opposite side of angle A is the side opposite to angle A, and the adjacent side is the side adjacent to angle A.

5. Finding the value of tg(A): - Since sin(A) = 9, we can conclude that the opposite side of angle A is 9. - In a right triangle, the hypotenuse is the longest side, and the adjacent side is the side adjacent to angle A. - Since angle C is 90 degrees, the hypotenuse is the side opposite to the right angle, and the adjacent side is the side adjacent to angle A. - Therefore, tg(A) = opposite/adjacent = 9/adjacent.

Unfortunately, the search results did not provide the necessary information to determine the value of the adjacent side or the exact value of tg(A). However, based on the given information, we can conclude that tg(A) is equal to 9 divided by the length of the adjacent side.

Please note that without the specific lengths of the sides of the triangle, we cannot determine the exact value of tg(A).