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
The distance would be equal to 2 times the longest side of the rectangle plus twice the shortest side multiplied by pi / 2 for the semicircle, that is:
longest side 96 and shortest 48
D = 2 * (96) + 2 * (1/2) * pi * 48
D = 192 + pi * 48
This shorter side, which starts at 48, will expand each time by two more in proportion to 20 of the running track between 8 than the number of divisions, that is, 2 * (20/8) = 5
In other words, there are 8 distances, like this:
D1 = 192 + 3.14 * 48 = 342.72 yd
D2 = 192 + 3.14 * (48 + 5) = 358.42 yd
D3 = 192 + 3.14 * (48 + 10) = 374.12 yd
D4 = 192 + 3.14 * (48 + 15) = 389.82 yd
D5 = 192 + 3.14 * (48 + 20) = 405.52 yd
D6 = 192 + 3.14 * (48 + 25) = 421.22 yd
D7 = 192 + 3.14 * (48 + 30) = 436.92 yd
D8 = 192 + 3.14 * (48 + 35) = 452.62 yd
The point-slope form:
m - slope
x₁, y₁ - the coordinates of a point
It passes through the points (1,-2) and (2,2).
Answer:
6th square -2
8th square -3
9th square -8
Step-by-step explanation: The sum is -12
Answer:
A
Step-by-step explanation:
3+7 is 10, not 11. Therefore, x cannot be 3.
