This is the question i dont rlly get

1. Consider the right triangle ABC given below.

lbvjy [14]

#1)
A) b = 10.57
B) a = 22.66; the different methods are shown below.
#2)
A) Let a = the side opposite the 15° angle; a = 1.35.
Let B = the angle opposite the side marked 4; m∠B = 50.07°.
Let C = the angle opposite the side marked 3; m∠C = 114.93°.
B) b = 10.77
m∠A = 83°
a = 15.11

Explanation
#1)
A) We know that the sine ratio is opposite/hypotenuse. The side opposite the 25° angle is b, and the hypotenuse is 25:
sin 25 = b/25

Multiply both sides by 25:
25*sin 25 = (b/25)*25
25*sin 25 = b
10.57 = b

B) The first way we can find a is using the Pythagorean theorem. In Part A above, we found the length of b, the other leg of the triangle, and we know the measure of the hypotenuse:
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

The second way is using the cosine ratio, adjacent/hypotenuse. Side a is adjacent to the 25° angle, and the hypotenuse is 25:
cos 25 = a/25

Multiply both sides by 25:
25*cos 25 = (a/25)*25
25*cos 25 = a
22.66 = a

The third way is using the other angle. First, find the measure of angle A by subtracting the other two angles from 180:
m∠A = 180-(90+25) = 180-115 = 65°

Side a is opposite ∠A; opposite/hypotenuse is the sine ratio:
a/25 = sin 65

Multiply both sides by 25:
(a/25)*25 = 25*sin 65
a = 25*sin 65
a = 22.66

#2)
A) Let side a be the one across from the 15° angle. This would make the 15° angle ∠A. We will define b as the side marked 4 and c as the side marked 3. We will use the law of cosines:
a² = b²+c²-2bc cos A
a² = 4²+3²-2(4)(3)cos 15
a² = 16+9-24cos 15
a² = 25-24cos 15
a² = 1.82

Take the square root of both sides:
√a² = √1.82
a = 1.35

Use the law of sines to find m∠B:
sin A/a = sin B/b
sin 15/1.35 = sin B/4

Cross multiply:
4*sin 15 = 1.35*sin B

Divide both sides by 1.35:
(4*sin 15)/1.35 = (1.35*sin B)/1.35
(4*sin 15)/1.35 = sin B

Take the inverse sine of both sides:
sin⁻¹((4*sin 15)/1.35) = sin⁻¹(sin B)
50.07 = B

Subtract both known angles from 180 to find m∠C:
180-(15+50.07) = 180-65.07 = 114.93°

B) Use the law of sines to find side b:
sin C/c = sin B/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 m∠A by subtracting both known angles from 180:
180-(52+45) = 180-97 = 83°

Use the law of sines to find side a:
sin C/c = sin A/a
sin 52/12 = sin 83/a

Cross multiply:
a*sin 52 = 12*sin 83

Divide both sides by sin 52:
(a*sin 52)/(sin 52) = (12*sin 83)/(sin 52)
a = 15.11

3 0

3 years ago

Read 2 more answers

I don’t know if it’s wrong or not

faltersainse [42]

I actually think that it is 50

5 0

3 years ago

How do I find slope intercept

Nastasia [14]

Answer:

This can be done by calculating the slope between two known points of the line using the slope formula.

This can be done by substituting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b.

4 0

3 years ago

The length of a sticky note measures 77 millimeters.express this length in meters explain your thinking include an equation with

Eva8 [605]

The length of the sticky notes is $\bf77\times{10^{-3}}{\text{meter}}$ .

Further explanation:

Given:

The length of sticky notes is measured as 77 millimeters.

Calculation:

Since 1 meter contains 1000 mm, it can be written as follows:

$\begin{aligned}1000{\text{mm}}&\to{\text{1meter}}\\{\text{1mm}}&\to\frac{{\text{1}}}{{1000}}{\text{meter}}\\{\text{1mm}}&\to{10^{-3}}{\text{meter}}\\x\,{\text{mm}}&\to x \times {10^{-3}}{\text{meter}} \\ \end{aligned}$

Now, substitute 77 for x in above expression to obtain the length of sticky notes in meter as follows:

$77\,{\text{mm}}\to77\times{10^{-3}}{\text{meter}}$

Thus, the length of the sticky notes is $\bf77\times{10^{-3}}{\text{meter}}$ .

Learn more:

1. Which function has an inverse that is also a function? {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}

brainly.com/question/1632445

2. A given line has the equation 10x + 2y = −2. what is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)? y = ( )x + 12

brainly.com/question/1473992

3. what are the domain and range of the function f(x) = 3x + 5?

brainly.com/question/3412497

Answer Details :

Grade: Middle School

Subject: Mathematics

Chapter: linear equation

Keywords:

Millimeters, meter, equation, sticky notes, measurements, length, function, substitution, Mexico, site, direct substitution, elimination, graph, middle term factorization, scientific notation.

3 0

3 years ago

Read 2 more answers

Given that cos (x) = 1/3, find sin (90 - x)

ddd [48]

Answer:

$\sin(90^{\circ} - x)=\frac{1}{3}$