Question

Катети прямокутного трикутника дорівнюють 5см і 12см, Знайдіть косинус кута проилежного меншому катету

Answer 1

Ответ:

tg = 12/5

1 + tg² = 1 / cos²

cos² = 1 / (1 + tg) = 1 / (17/5) = 5/17

cos = √(5/17)

Answer 2

Finding the Cosine of the Angle Opposite the Smaller Leg

To find the cosine of the angle opposite the smaller leg in a right triangle, we can use the relationship between the sides of a right triangle and the trigonometric functions.

Given that the lengths of the legs of the right triangle are 5 cm and 12 cm, we can find the cosine of the angle opposite the smaller leg.

Using the Pythagorean theorem, we can find the length of the hypotenuse (c) of the right triangle:

\(c^2 = a^2 + b^2\)

where a and b are the lengths of the legs.

Substituting the given values, we have:

\(c^2 = 5^2 + 12^2\)

Simplifying, we get:

\(c^2 = 25 + 144\)

\(c^2 = 169\)

Taking the square root of both sides, we find:

\(c = 13\)

Now, we can find the cosine of the angle opposite the smaller leg (let's call it angle A) using the formula:

\(\cos(A) = \frac{b}{c}\)

Substituting the values, we have:

\(\cos(A) = \frac{5}{13}\)

Therefore, the cosine of the angle opposite the smaller leg is 5/13.