Question

У прямокутному трикутнику трикутнику катет = 3 см і 8 см. Знайти тангенс гстрого кута який лежить проти меншого катета

Answer 1

В прямоугольном треугольнике  катет b=3 см и a=8 см.
Tангенс острого угла который лежит против меньшего катета:
tg α=b/a=3/8=0,375

Answer 2

Тангенс острого угла, лежащего напротив меньшего катета равен отношению противолежащего катета к прилежащему, то есть tgα=3/8

Answer 3

Problem Analysis

We are given a right triangle with two sides, the legs, measuring 3 cm and 8 cm. We need to find the tangent of the acute angle that is opposite the smaller leg.

Solution

To find the tangent of an angle in a right triangle, we can use the ratio of the length of the opposite side to the length of the adjacent side. In this case, the smaller leg is the adjacent side and the opposite side is the side we are interested in.

Let's label the sides of the triangle: - The smaller leg (adjacent side) is labeled as 'a' and measures 3 cm. - The larger leg (opposite side) is labeled as 'b' and measures 8 cm.

We can use the tangent function to find the tangent of the angle opposite the smaller leg: tan(angle) = opposite/adjacent = b/a

Substituting the given values, we have: tan(angle) = 8/3

Now, let's calculate the value of the tangent of the angle.

Calculation

Using the given values, we can calculate the tangent of the angle as follows: tan(angle) = 8/3 ≈ 2.6667

Therefore, the tangent of the acute angle that is opposite the smaller leg is approximately 2.6667.

Answer

The tangent of the acute angle that is opposite the smaller leg in the given right triangle is approximately 2.6667.