-- You have two angles.
-- They're complementary . . . they add up to 90 degrees.
-- One is 4 times as big as the other one.
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-- The smaller angle has 1 share of the 90 degrees.
-- The bigger angle has 4 shares of the 90 degrees.
-- (The smaller one is 1/4 the size of the bigger one.
The bigger one is 4 times the size of the smaller one.)
-- When you add them together, you get 5 shares, totaling 90 degrees.
-- What's the size of each share ? It's 90/5 = 18 degrees.
-- The smaller angle gets one share . . . 18 degrees.
-- The bigger angle gets 4 shares. (4 x 18) = 72 degrees.
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Check:
-- Is the small one 1/4 the size of the big one ? 18/72 = 1/4 Yes.
-- Are they complementary ? Do they add up to 90 degrees ?
18 + 72 = 90 Yes.
yay !
H=how far up from the ground does the ladder touch the building
h/30=sin 25°
h=30 sin 25°
h=12.7 decimeters(1 decimal place)
Answer: The height that the ladder touch the building far up from the ground is 12.7 decimeters.
Hi!
<h3>To find the prime factorization of a number, keep dividing by the smallest factor that goes into it. </h3>
63/3 = 21
21/3 = 7
7/7 = 1
<u>3 · 3 · 7 = 63</u>
<h2>The answer is D. 3 · 3 · 7 </h2>
Hope this helps! :)
-Peredhel
Step-by-step explanation:
a.
2(3x) - 5x = 4
6x - 5x = 4
x = 4
B. -5(x-4)+8x=29
-5x+20+8x=29
3x+20=29
3x=9
x=3
C. 2y=18+2(3-y)
2y=18+6-2y
2y=24-2y
4y=24
y=6
D. c = -b - 11
3c + 6 = 6b
3( -b - 11) +6 = 6b
-3b-33+6=6b
-3b-27=6b
-27=9b
3=b
Explanation:
The Law of Sines is your friend, as is the Pythagorean theorem.
Label the unmarked slanted segments "a" and "b" with "b" being the hypotenuse of the right triangle, and "a" being the common segment between the 45° and 60° angles.
Then we have from the Pythagorean theorem ...
b² = 4² +(2√2)² = 24
b = √24
From the Law of Sines, we know that ...
b/sin(60°) = a/sin(θ)
y/sin(45°) = a/sin(φ)
Solving the first of these equations for "a" and the second for "y", we get ...
a = b·sin(θ)/sin(60°)
and ...
y = a·sin(45°)/sin(φ)
Substituting for "a" into the second equation, we get ...
y = b·sin(θ)/sin(60°)·sin(45°)/sin(φ) = (b·sin(45°)/sin(60°))·sin(θ)/sin(φ)
So, we need to find the value of the coefficient ...
b·sin(45°)/sin(60°) = (√24·(√2)/2)/((√3)/2)
= √(24·2/3) = √16 = 4
and that completes the development:
y = 4·sin(θ)/sin(φ)
