Answer:
Error was CHOOSING the CORRECT hypotenuse in the given sides.
H = 41 units
Step-by-step explanation:
Here, the given sides of the triangle are: 41,40 and 9
Now, as we know in a RIGHT ANGLED TRIANGLE:
The longest side is the HYPOTENUSE.
So, here H = 41
Now, by PYTHAGORAS THEOREM:
Hence, Pythagoras theorem for Right angled triangle is SATISFIED
So, error was CHOOSING the CORRECT hypotenuse in the given sides.
The correct H = 41 units and NOT 40 units.
Answer:
a. 5% of the employees will experience lost-time accidents in both years
b. 24% of the employees will suffer at least one lost-time accident over the two-year period
Step-by-step explanation:
a. What percentage of the employees will experience lost-time accidents in both years?
20% last year, of those who suffered last year, 25% during this year. So
5% of the employees will experience lost-time accidents in both years.
b. What percentage of the employees will suffer at least one lost-time accident over the two-year period?
5% during the two years.
10% during the current year. 25% of employees who had lost-time accidents last year will experience a lost-time accident during the current year.
So the 10% is composed of 5% during both years(25% of 20%) and 5% of the 80% who did not suffer during the first year.
First year yes, not on the second.
75% of 20%. So, total:
24% of the employees will suffer at least one lost-time accident over the two-year period
Answer:
a) a = 7.37, b = 15.13, C = 67°
b) 1 triangle
Step-by-step explanation:
<h3>a)</h3>Two angles and one side are given. That means the triangle is uniquely determined, and the remaining sides can be found from the Law of Sines.
The third angle is ...
C = 180° -A -B = 180° -29° -84° = 67°
Then the Law of Sines tells you ...
a/sin(A) = b/sin(B) = c/sin(C)
a = sin(A)/sin(C)·c = sin(29°)/sin(67°)·14 ≈ 7.37
b = sin(B)/sin(C)·c = sin(84°)/sin(67°)·14 ≈ 15.13
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<h3>b)</h3>Ordinarily, when the given angle (B = 30°) is opposite the shorter of the given sides (b = 10 < a = 20), it means there are two possible solutions to the triangle.
However, when the sine of the angle is exactly equal to the ratio of the given sides: sin(30°) = 10/20 = 1/2, the larger angle can only be 90°. That is, the one triangle that can be formed is a right triangle.
The Law of Sines tells you this.
sin(A)/a = sin(B)/b
sin(A) = (a/b)sin(B) . . . . . . multiply by 'a'
A = arcsin(a/b·sin(B)) = arcsin(20/10·sin(π/6)) = arcsin(1)
A = 90°
