Question

Номер 596- НУЖНО РЕШЕНИЕ КАК МОЖНО БЫСТРЕЕ-ПОЖАЛУЙСТА; В прямоугольном треугольнике гипотенуза равна с, а один из острых углов равен @. выразите второй острый угол и катеты через с и @ и найдите их значения,если с=24 см, а @=35 градусов.

Answer 1

∠B=180-∠C-∠α
cosα=AC/c  AC=c*cosα=24*cos35°=24*0,82=19,68≈20
sinα=BC/c     BC=C*sinα=24*0,57=13.68≈14

Answer 2

Finding the Solution for the Given Problem

To find the solution for the given problem, we need to express the second acute angle and the legs of the right triangle in terms of the hypotenuse (c) and the given angle (@), and then calculate their values.

Expressing the Second Acute Angle and the Legs

In a right triangle, the sum of the two acute angles is always 90 degrees. Therefore, the second acute angle can be expressed as:

Second Acute Angle = 90 degrees - @ The legs of the right triangle can be expressed using trigonometric ratios. Let's denote the legs as a and b. The given angle (@) is opposite to one of the legs, and the hypotenuse (c) is opposite to the right angle. Therefore, we can use the following trigonometric ratios:

sin(@) = a / c cos(@) = b / c

Calculating the Values

Given: c = 24 cm @ = 35 degrees

To find the second acute angle, we can substitute the given value of @ into the formula:

Second Acute Angle = 90 degrees - 35 degrees = 55 degrees

To find the values of the legs (a and b), we can use the trigonometric ratios. Substituting the given values into the formulas:

sin(35 degrees) = a / 24 cm

Solving for a:

a = 24 cm * sin(35 degrees)

a ≈ 13.79 cm

cos(35 degrees) = b / 24 cm

Solving for b:

b = 24 cm * cos(35 degrees)

b ≈ 19.61 cm

Therefore, in the given right triangle with a hypotenuse of 24 cm and an angle of 35 degrees, the second acute angle is approximately 55 degrees, and the lengths of the legs are approximately 13.79 cm and 19.61 cm.

I hope this helps! Let me know if you have any further questions.