Question

У прямокутному трикутнику АВС, кут С дорівнює 90°. Катет ВС=28 см. Кут В дорівнює 60°. Знайти гіпотенузу АВ.

Answer 1

Ответ:

Гипотенуза  ВА =56 см

Объяснение:

Сначала найдем величину угла А

180-90-60= 30

Катет лежит напротив угла в 30 градусов, значит он равен половине гипотенузы. Гипотенуза = 28*2= 56 см

Answer 2

Problem Analysis

We are given a right triangle ABC, where angle C is 90°. We are also given that side BC (the side opposite angle C) is 28 cm, and angle B is 60°. We need to find the length of side AB (the hypotenuse).

Solution

To find the length of side AB, we can use the trigonometric function cosine. The cosine of angle B is defined as the ratio of the length of the adjacent side (AB) to the length of the hypotenuse (BC).

Using the given information, we can set up the equation:

cos(B) = AB / BC

Substituting the known values:

cos(60°) = AB / 28 cm

To find the value of cos(60°), we can refer to a trigonometric table or use a calculator. The cosine of 60° is 0.5.

0.5 = AB / 28 cm

To solve for AB, we can multiply both sides of the equation by 28 cm:

0.5 * 28 cm = AB

AB = 14 cm

Therefore, the length of side AB (the hypotenuse) is 14 cm.

Conclusion

In a right triangle ABC, where angle C is 90°, side BC is 28 cm, and angle B is 60°, the length of side AB (the hypotenuse) is 14 cm.