1. Consider the right triangle ABC given below. a. Find the length of side b to two decimal places.
b. Find the length of side a to two decimal places in three different ways.
2. Solve the triangles below.
Answers
A) b = 10.57
B) a = 22.66
#2)
A) a = 1.35 (across from the 15° angle)
∠C = 50.07° (the angle at the top of the triangle)
∠B = 114.93°
B) ∠A = 83°
b = 10.77 (across from angle B)
a = 15.11 (across from angle A)
Explanation
#1)
A) Since b is across from the 25° angle and we have the hypotenuse, we have the information for the sine ratio (opposite/hypotenuse):
sin 25 = b/25
Multiply both sides by 25:
25*sin 25 = (b/25)*25
25*sin 25 = b
10.57 = b
B) We will first use the cosine ratio. Side a is the side adjacent to the angle and we have the hypotenuse, and the cosine ratio is adjacent/hypotenuse:
cos 25 = a/25
Multiply both sides by 25:
25*cos 25 = (a/25)*25
25*cos 25 = a
22.66 = a
Now we will use the Pythagorean theorem. We know from part a that side b = 10.57, and the figure has a hypotenuse of 25:
a²+(10.57)² = 25²
a² + 111.7249 = 625
Subtract 111.7249 from both sides:
a²+111.7249-111.7249=625-111.7249
a² = 513.2751
Take the square root of both sides:
√a² = √513.2751
a = 22.66
#2)
A) Let A be the 15° angle, B be the angle to the right and C be the angle at the top of the triangle. This means side a is across from angle A, side B is across from angle B, and side c is across from angle C.
Using the law of cosines,
a²=3²+4²-2(3)(4)cos(15)
a²=9+16-24cos(15)
a²=25-24cos(15)
a²=1.8178
Take the square root of both sides:
√a² = √1.8178
a = 1.3483≈1.35
Now we can use the Law of Sines to find angle C:
sin 15/1.35 = sin C/4
Cross multiply:
4*sin 15 = 1.35* sin C
Divide both sides by 1.35:
(4*sin 15)/1.35 = (1.35*sin C)/1.35
(4*sin 15)/1.35 = sin C
Take the inverse sine of both sides:
sin⁻¹((4*sin 15)/1.35) = sin⁻¹(sin C)
sin⁻¹((4*sin 15)/1.35) = C
50.07 = C
To find angle B, add angle A and angle C together and subtract from 180:
B=180-(50.07+15) = 180-65.07 = 114.93
B) To find angle A, add angle B and angle C together and subtract from 180:
180-(52+45) = 180-97 = 83
Now use the Law of Sines to find side b (across from angle B):
sin 52/12 = sin 45/b
Cross multiply:
b*sin 52 = 12*sin 45
Divide both sides by sin 52:
(b*sin 52)/(sin 52) = (12*sin 45)/(sin 52)
b = 10.77
Find side a using the Law of Sines:
sin 83/a = sin 52/12
Cross multiply:
12*sin 83 = a*sin 52
Divide both sides by sin 52:
(12*sin 83)/(sin 52) = (a*sin 52)/(sin 52)
15.11 = a
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Find the sum: (3x2 + 5x − 8) + (5x2 − 13x − 5)8x2 + 8x − 13 8x2 − 8x + 13 8x2 − 8x − 13 8x2 − x − 13
Answers
O O and N are similar and congruent.
OM and N are similar but not congruent.
OM and O are similar but not congruent.
Answers
Answer:
D.
Step-by-step explanation:
Answers
Answer:
-1.714001255
Step-by-step explanation:
Well just plug it in your calculator.
Answers
Answer:
The total income is 257,250
Step-by-step explanation:
The initial value of salary is 36,000 a year with an increase of 250 every year. Next is presented the salary table of each year:
Year Salary
- 36,000
- 36,250
- 36,500
- 36,750
- 37,000
- 37,250
- 37,500
To have the total income you have to sum all the value of the seven years.
Total income = 36,000 + 36,250 + 36,500 + 36,750 + 37,000 + 37,250 + 37,500 = 257,250 is the total income for the 7 years.
Answers
The graph of the function is a parabola.
The nose comes down as far as y=4 but no farther.
That happens when (x - 2)² = 0 , and THAT happens when x = 2 .
f(x) = (x - 2)(x - 2) + 4
f(x) = (x(x - 2) - 2(x - 2)) + 4
f(x) = (x(x) - x(2) - 2(x) + 2(2)) + 4
f(x) = (x² - 2x - 2x + 4) + 4
f(x) = (x² - 4x + 4) + 4
f(x) = x² - 4x + 4 + 4
f(x) = x² - 4x + 8
Answers
Answer: y = -2x + 13.
Step-by-step explanation:
To find the equation of a line that passes through the points (4,5) and (2,9), we can follow these steps:
1. First, let's determine the slope of the line using the formula: slope (m) = (change in y) / (change in x). We can choose any point as (x1, y1) and the other point as (x2, y2) to calculate the slope.
Using (4,5) as (x1, y1) and (2,9) as (x2, y2):
slope (m) = (5 - 9) / (4 - 2) = -4 / 2 = -2
2. Now that we have the slope (-2), we can use the point-slope form of a line to find the equation. The point-slope form is given by: y - y1 = m(x - x1), where (x1, y1) is one of the given points and m is the slope.
Using (4,5) as (x1, y1) and -2 as the slope (m):
y - 5 = -2(x - 4)
3. Simplifying the equation further, we get:
y - 5 = -2x + 8
4. To obtain the equation in slope-intercept form, we can isolate y by adding 5 to both sides:
y = -2x + 8 + 5
y = -2x + 13
Therefore, the equation of the line that passes through the points (4,5) and (2,9) is y = -2x + 13.
Final answer:
The equation of the line that passes through the points (4,5) and (2,9) is y = x + 1.
Explanation:
To find the equation of the line that goes through the two given points (4,5) and (2,9), we can use the slope-intercept form of a linear equation, y = mx + b.
First, we need to calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values from the points, we get:
m = (9 - 5) / (2 - 4) = -2 / -2 = 1.
Next, we can substitute the slope and one of the given points into the equation to solve for the y-intercept (b).
Using the point (4,5):
5 = (1)(4) + b
b = 5 - 4 = 1.
Therefore, the equation of the line is y = x + 1.
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