Will give Brainliest!! pleases help, math. 1. Solve triangle ABC if A = 50°, a = 10, and b = 20. If no triangle exists, explain why.

2. Solve triangle ABC if A = 65°, B = 65°, and c = 6. If no triangle exists, explain why.

3. A surveyor is trying to find the length of a lake. He finds a baseline distance AB
of 125 m. Angle A is measured to be 41.6° and angle B is measured at 124.3°.
Find the length of the lake d.

a = sqrt(b^2 + c^2 - 2bc cosA) = sqrt(13^2 + 6^2 - 2 * 13 * 6 * cos 50) = sqrt(169 + 36 - 156 cos 50) ≈ sqrt(205 - 100.3) ≈ sqrt(104.7) ≈ 10.2

a ≈ 10.2

c / sin C = a / sin A

sin C = c sin A / a = 6 sin 50 / 10.2 ≈ 0.4491

C = arcsin(0.4491) ≈ 26.7

C ≈ 26.7°

B = 180 - A - C ≈ 180 - 50 - 26.7 ≈ 103.3

B ≈ 103.3°

Step-by-step explanation:

___Y/X : ___ 1 ___ 2 3 __total

1 1/9 __ 1/9 ___1/9 __ 1/3

21/9 __ 1/9 ___1/9 __ 1/3

31/9 __ 1/9 ___1/9 __ 1/3

___Total __ 1/3 __ 1/3 ___ 1/3 __ 1

Y: 1 2 3

P(Y) : _ 1/3 1/3 1/3

μXY = E(X) * E(Y) = 2 * 2 = 4

Cov(X, Y) = 0

Step-by-step explanation:

Sample space = 3² = 9

___Y/X : ___ 1 ___ 2 3 __total

1 1/9 __ 1/9 ___1/9 __ 1/3

21/9 __ 1/9 ___1/9 __ 1/3

31/9 __ 1/9 ___1/9 __ 1/3

___Total __ 1/3 __ 1/3 ___ 1/3 __ 1

The probability density function :

X : __ 1 2 3

P(X) : 1/3 ___1/3 1/3

μX =E(X) = ΣX*P(X) = (1*1/3) + (2*1/3) * (3*1/3)

= 1/3 + 2/3 + 1 = (1 + 2 + 3) / 3 = 6/3 = 2

Y: 1 2 3

P(Y) : _ 1/3 1/3 1/3

μY =E(Y) = ΣY*P(Y) = (1*1/3) + (2*1/3) * (3*1/3)

= 1/3 + 2/3 + 1 = (1 + 2 + 3) / 3 = 6/3 = 2

μXY = E(X) * E(Y) = 2 * 2 = 4

Cov(X, Y) = 0

X and Y are independent