Solve the problems below. Please answer with completely simplified exact value(s) or expression(s). Given: ΔАВС, m∠ACB = 90° CD
⊥ AB , m∠ACD = 60°,BC = 6 cm Find CD, Area of ΔABC
PICTIURE:https://homework.russianschool.com/resource?key=00j42
PICTIURE:https://homework.russianschool.com/resource?key=00j42
1 answer:
Answer:
Step-by-step explanation:
Triangle ABC is right triangle. Since m∠ACB = 90° and m∠ACD = 60°, you get m∠BCD = 90°-60°=30°.
Triangle BCD is rigth triangle, then the leg that is opposite to the angle of 30° is half of the hypotenuse. Thus,
By the Pythagorean theorem,
Then
Hypotenuse AB of the triangle ABC is equal to
The area of the triangle ABC is
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The answer is 7.9306
Using the formula in the attached:
Where: xi = sample value; μ = sample mean; n = sample size
1.) Calculate the mean first:
μ = 12.0 + 18.3 + 29.6 + 14.3 + 27.8 / 5
= 102 / 5
μ = 20.4
2.) Using the mean, calculate (xi - μ)² for each value:
(12.0 - 20.4)² = 70.56
(18.3 - 20.4)² = 4.41
(29.6 - 20.4)² = 84.64
(14.3 - 20.4)² = 37.21
(27.8 - 20.4)² = 54.76
3.) Sum the squared differences and divide by n - 1.
μ = 70.56 + 4.41 + 84.64 + 37.21 + 54.76
= 251.58 / 5-1
μ = 62.895 (this is now called sample variance)
4.) Get the square root of the sample variance:
√62.895 = 7.9306
Using the formula in the attached:
Where: xi = sample value; μ = sample mean; n = sample size
1.) Calculate the mean first:
μ = 12.0 + 18.3 + 29.6 + 14.3 + 27.8 / 5
= 102 / 5
μ = 20.4
2.) Using the mean, calculate (xi - μ)² for each value:
(12.0 - 20.4)² = 70.56
(18.3 - 20.4)² = 4.41
(29.6 - 20.4)² = 84.64
(14.3 - 20.4)² = 37.21
(27.8 - 20.4)² = 54.76
3.) Sum the squared differences and divide by n - 1.
μ = 70.56 + 4.41 + 84.64 + 37.21 + 54.76
= 251.58 / 5-1
μ = 62.895 (this is now called sample variance)
4.) Get the square root of the sample variance:
√62.895 = 7.9306