We'll use standard labeling of right triangle ABC, C=90 degrees, legs a, b, hypotenuse c.
11.
Right triangle, cliff peak A, boat B, angle opposite cliff is B=28.9 deg. adjacent leg a=65.7 m, cliff height is leg b.
tan B = b/a
b = a tan B = 65.7 tan 28.9° = 36.3 m
12.
Similar story, boat at B, opposite b=3.5 m, rope c=12 m
sin B = b/c
B = arcsin b/c = arcsin (3.5/12) = 17.0°
13.
c=124 m, A=58°
sin A = a/c
a = c sin A = 124 sin 58 = 105.2 m
14.
That's a hypotenuse c=4-1.2 = 2.8 m to a height b=1.8m so
cos A = b/c
A = arccos b/c = arccos (1.8/2.8) = 50.0°
15.
Not a right triangle, an isosceles triangle. Half of it is a right triangle with hypotenuse one arm, c=9.8 cm and angle opposite half the base of B=62/2=31°. We're after d=2b:
sin B = b/c
b = c sin B
d = 2b = 2 c sin B = 2(9.8) sin 31 = 10.1 cm
Almost equilateral
1/3 or 5/6
Lets make the fractions into decimals. To make a fraction into decimal you have to divide the numerator by the denominator. The numerator is the top part of a fraction and the denominator is the bottom part of the fraction.
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Calculations
1/3
1 ÷ 3 = 0.3333....
5/6
5 ÷ 6 = 0.83333...
0.83333... is greater then 0.3333.....
Therefore 5/6 is greater then 1/3
1/3 is smaller then 5/6
True because they are both constants.
Answer:
24:40 or 3:5
Step-by-step explanation:
Boys: 24
All children: 24 + 16 = 40
Boys to total amount of children: 24:40
Simplify: 24:40 = 3:5
I believe that would be 1
