Question

2.48. Найдите неизвестные стороны и острые углы пря- моугольного треугольника по следующим данным: 1) по двум катетам: a) a = 3, b = 4; б) а = 9, b = 10; B) a=20, ь - г) а = 11, b = 60; д) а = 6, b = 8; e) a = 5, b = 1: 2) по гипотенузе и катету: a) c = 13, a = 5; в) c = 17, а = 25, a = 7; г) 0 = 85, а = 84. 14*5 6) d = 25, a = 50°20'; г) c = 16, a = 76°21'. углу: б) а = 5, а = 40°48'; г) а = 9, а = 68°.​

Answer 1

Відповідь:

Пояснення:

To find the unknown sides and angles in a right-angled triangle, the Pythagorean theorem and trigonometric functions can be used.

Given two legs:

a) a = 3, b = 4, c = sqrt(a^2 + b^2) = 5

Angle A can be found using the tangent function: tan A = b/a = 4/3.

b) a = 9, b = 10, c = sqrt(a^2 + b^2) = 15

Angle A can be found using the tangent function: tan A = b/a = 10/9.

c) a = 20, b = sqrt(c^2 - a^2) = sqrt(400 - 400) = sqrt(0) = 0

Angle A can be found using the tangent function: tan A = b/a = 0/20.

d) a = 11, b = 60, c = sqrt(a^2 + b^2) = 61

Angle A can be found using the tangent function: tan A = b/a = 60/11.

e) a = 5, b = 1, c = sqrt(a^2 + b^2) = sqrt(26) = 5.1

Angle A can be found using the tangent function: tan A = b/a = 1/5.

Given hypotenuse and leg:

a) c = 13, a = 5, b = sqrt(c^2 - a^2) = sqrt(169 - 25) = sqrt(144) = 12

Angle A can be found using the tangent function: tan A = b/a = 12/5.

b) c = 17, a = 7, b = sqrt(c^2 - a^2) = sqrt(289 - 49) = sqrt(240) = 15

Angle A can be found using the tangent function: tan A = b/a = 15/7.

c) c = 85, a = 84, b = sqrt(c^2 - a^2) = sqrt(7225 - 7056) = sqrt(169) = 13

Angle A can be found using the tangent function: tan A = b/a = 13/84.

d) c = 25, A = 50°20', a = c * cos A = 25 * cos 50°20'

b = c * sin A = 25 * sin 50°20'

e) c = 16, A = 76°21', a = c * cos A = 16 * cos 76°21'

b = c * sin A = 16 * sin 76°21'

Given leg and angle:

a) a = 5, A = 40°48', c = sqrt(a^2 / (tan A)^2 + a^2) = sqrt(25 / (tan 40°48')^2 + 25)

b = a * tan A = 5 * tan 40°48'

b) a = 9, A = 68°, c = sqrt(a^2 / (tan A)^2 + a^2) = sqrt(81 / (tan 68°)^2 + 81)

b = a * tan A = 9 * tan 68°