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
4.3-1.4(p+7)=-9.7
4.3-1.4p-9.8=9.7
4.3-1.4p=0.1
-1.4p=-4.2
p=3
Hope this helps :)
Answer:
Flora can make 10 pairs of socks and 5 pairs of gloves.
Step-by-step explanation:
Here we have to form two equations from the given information.
Let "x" be the number of pair of socks and "y" be the number of pair of gloves.
Given:
It takes flora 3 hours to knit a pair of socks and 7 hours to knit a pair of gloves. If she spent 65 hours knitting a total of 15 pairs of socks and gloves,
x + y = 15
3x + 7y = 65
Now we have to solve these two equations to find the solution.
Let's use the substitution method.
From the first equation can be written as
x = 15 - y
Now plug in x = 15 - y in the second equation and find the value of y.
3(15 - y) + 7y = 65 (This is called substitution method)
45 - 3y + 7y = 65
Simplify the like terms
45 + 4y = 65
Subtract 45 from both sides, we get
4y = 65 - 45
4y = 20
Dividing both sides by 4, we get
y = 20/4
y = 5
Now plug in y = 5 in the x = 15 - y
x = 15 - 5
x = 10
Therefore, Flora can make 10 pairs of socks and 5 pairs of gloves.
Step 1) Add up the three given angles: 125+109+83 = 317
Step 2) Subtract the result (found in step one) from 360
360 - 317 = 43
The reason for the 360 is because for any four-sided polygon, the angles always add up to 360 degrees.
The answer is 43
