In ΔFGH, the measure of ∠H=90°, the measure of ∠G=21°, and FG= 9 feet. Find the length of GH to the nearest tenth of a foot.
Answers
Answer: 8.4 feet
Step-by-step explanation:
In ΔFGH, the measure of ∠H=90°, the measure of ∠G=21°, and FG = 9 feet. Find the length of GH to the nearest tenth of a foot.
F
G
H
x
9
(opposite of ∠G)
(adj. to ∠G)
(hypotenuse)
21°
\text{What function uses the HYPOTENUSE and the ADJACENT?}
What function uses the HYPOTENUSE and the ADJACENT?
\text{SOH-CAH-TOA}
SOH-CAH-TOA
\cos G = \frac{\text{adjacent}}{\text{hypotenuse}}=\frac{x}{9}
cosG=
hypotenuse
adjacent
=
9
x
\cos 21=\frac{x}{9}
cos21=
9
x
9\cos 21=x
9cos21=x
Cross multiply.
x=8.4022\approx \mathbf{8.4}\text{ feet}
x=8.4022≈8.4 feet
Type into calculator and roundto the nearest tenth of a foot.
F
G
H
8.4
9
(opposite of ∠G)
(adj. to ∠G)
(hypotenuse)
21°
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= 0.29 x 9.8
= 2.842 N
Answer:
2.842 N
Step-by-step explanation:
Newton's second law is given by the equation
Where,
- F is the force in Newtons
- m is the mass in kilograms (kg)
- a is acceleration given in meters per second squared
Given in the problem,
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Substituting into the formula gives us F:
Newtons (N)
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Answers
Answers
Answer: 3/4
================================================
Explanation
The point (p,r) is on the line y = x+b
Plug in x = p and y = r to get r = p+b. Let's solve for b
r = p+b
b = r-p
This will be used later.
The point (2p,5r) is on the line y = 2x+b
Plug in those coordinates:
y = 2x+b
5r = 2*(2p)+b
5r = 4p+b
Next we replace b with r-p. This is valid because b = r-p.
5r = 4p+b
5r = 4p+r-p
5r = 3p+r
5r-r = 3p
4r = 3p
Then we follow the cross multiplication process in reverse.
4r = 3p
4r/4 = 3p/r
r = 3p/4
r/p = (3p/4)*(1/p)
r/p = 3/4 is the final answer
Final answer:
Using the given coordinates and equations, we find that the value of r/p is 3/4 after a process of subtracting and simplifying two equations.
Explanation:
The question is related to the linear equations in the xy-plane. Given two points, (p,r) and (2p,5r) which lie respectively on the equations y = x + b and y = 2x + b.
We have two points on two different lines:
- Point A: (p, r) lies on the line y = x + b.
- Point B: (2p, 5r) lies on the line y = 2x + b.
Substituting the coordinates of the first point into the first equation gives r = p + b. Similarly, substituting the coordinates of the second point into the second equation gives 5r = 2(2p) + b, which simplifies to 5r = 4p + b.
Now, subtract the first equation from the second to eliminate b, resulting in 5r - r = 4p - p, which simplifies to 4r = 3p.
Dividing by 4p gives us r/p = 3/4. So, the value of r/p is 3/4.
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