Question

найдите гипотенузу и острые углы прямоугольного треугольника,если его катеты равны 20см и 21см.

Answer 1

a=20

b=21

c=√21²+20²=√441+400=√841=29

a/SinA=b/SinB=c/SinC

20/SinA=29/Sin90

SinA=20/29≈ 0.6896

угол A = 43⁰36'

21/SinB=29/Sin90

SinB=21/29≈0.7241

угол B = 46⁰24'

Answer 2

Finding the Hypotenuse and Angles of a Right-Angled Triangle

To find the hypotenuse and acute angles of a right-angled triangle with the given side lengths of 20 cm and 21 cm, we can use the Pythagorean theorem and trigonometric functions.

Hypotenuse (c): The hypotenuse of a right-angled triangle can be found using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is: c^2 = a^2 + b^2

Using the given side lengths: - a = 20 cm - b = 21 cm

We can calculate the hypotenuse (c) using the Pythagorean theorem: c^2 = 20^2 + 21^2 c^2 = 400 + 441 c^2 = 841 c = √841 c = 29 cm

Acute Angles: The acute angles of a right-angled triangle can be found using trigonometric functions. The sine, cosine, and tangent of an angle in a right-angled triangle can be calculated using the ratios of the triangle's sides.

Let's denote the acute angles as angle A and angle B, where: - A is the angle opposite side a - B is the angle opposite side b

We can use the following trigonometric relationships: - sin(A) = a / c - cos(A) = b / c - tan(A) = a / b - sin(B) = b / c - cos(B) = a / c - tan(B) = b / a

Using the calculated hypotenuse (c = 29 cm) and the given side lengths: - a = 20 cm - b = 21 cm

We can calculate the acute angles A and B using the trigonometric functions.

Let's calculate the acute angles: - sin(A) = 20 / 29 - cos(A) = 21 / 29 - tan(A) = 20 / 21 - sin(B) = 21 / 29 - cos(B) = 20 / 29 - tan(B) = 21 / 20

These calculations will give us the values of the acute angles A and B.

This information will help us find the hypotenuse and acute angles of the given right-angled triangle with side lengths of 20 cm and 21 cm.