Question

Найти синус косинус тангенс углов а и в треугольника авс с прямым углом с если ав=8см св=4 см

Answer 1

I hope this helps you

Answer 2

Теорема пифагора
АС²=АВ²-СВ²=48
АС=√48=4√3
угол А
$sin= \frac{4}{8} = \frac{1}{2} \\ cos= \frac{ 4\sqrt{3} }{8} = \frac{ \sqrt{3} }{2} \\ tg= \frac{4}{4 \sqrt{3} } = \frac{1}{ \sqrt{3} } \\ ctg= \sqrt{3}$
угол В
$sin= \frac{4 \sqrt{3} }{8} = \frac{ \sqrt{3} }{2} \\ cos= \frac{4}{8} = \frac{1}{2} \\ tg= \frac{4 \sqrt{3} }{4} = \sqrt{3} \\ ctg= \frac{1}{ \sqrt{3} }$

Answer 3

Finding Trigonometric Functions in a Right-Angled Triangle

To find the sine, cosine, and tangent of angles A and B in triangle ABC with a right angle at C, where AB = 8 cm and BC = 4 cm, we can use the following trigonometric functions:

Sine (sin): The sine of an angle in a right-angled triangle is calculated as the ratio of the length of the side opposite the angle to the length of the hypotenuse.

Cosine (cos): The cosine of an angle in a right-angled triangle is calculated as the ratio of the length of the adjacent side to the angle to the length of the hypotenuse.

Tangent (tan): The tangent of an angle in a right-angled triangle is calculated as the ratio of the length of the side opposite the angle to the length of the adjacent side.

Using the given information, we can calculate the trigonometric functions for angles A and B in triangle ABC.

Calculating Trigonometric Functions

Using the Pythagorean theorem, we can find the length of the hypotenuse AC: - AC^2 = AB^2 + BC^2 - AC^2 = 8^2 + 4^2 - AC^2 = 64 + 16 - AC^2 = 80 - AC = √80 - AC ≈ 8.94 cm

Now, we can calculate the trigonometric functions for angles A and B using the lengths of the sides of the triangle.

For Angle A: - Sin(A) = Opposite / Hypotenuse = BC / AC = 4 / 8.94 - Cos(A) = Adjacent / Hypotenuse = AB / AC = 8 / 8.94 - Tan(A) = Opposite / Adjacent = BC / AB = 4 / 8

For Angle B: - Sin(B) = Opposite / Hypotenuse = AB / AC = 8 / 8.94 - Cos(B) = Adjacent / Hypotenuse = BC / AC = 4 / 8.94 - Tan(B) = Opposite / Adjacent = AB / BC = 8 / 4

Results

Using the above calculations, we find the trigonometric functions for angles A and B in triangle ABC with a right angle at C: - Sin(A) ≈ 0.447 - Cos(A) ≈ 0.894 - Tan(A) = 0.5 - Sin(B) ≈ 0.894 - Cos(B) ≈ 0.447 - Tan(B) = 2

These values represent the sine, cosine, and tangent of angles A and B in the given right-angled triangle ABC.