Ask question

Ask question

All categories

2 years ago

10

Ivy is running errands for her mother. She bikes along straight paths to the supermarket, the bank, and then back home.Find the

distance between Ivy's house and the supermarket and the distance between the supermarket and the bank. Each distance is rounded to the nearest meter.

1 answer:

chubhunter [2.5K]2 years ago

5 0

The distance between Ivy's house and the supermarket and the distance between the supermarket and the bank:
H&S = 1,014 M; and S&B = 854m. This is resolved using the Sine Theorem.

<h3>What is the calculation backing the above solution?</h3>

Notice that the Angles of a Triangle add up to 180° That is

∠A + ∠B + ∠C = 180°

Thus,

∠C = 180° - 32° - 109°

= 39°

Recall the Sine Theorem which indicates;

a/SinA = b/SinB = c/SinC

thus given that

AC = 1,523m

We have

AC/SinB = BC/SinA

BC = AC/SinB * SinA

= 1523/Sin109° * Sin32°

BC =854m

Therefore

AC/SinB = AB/SinC
Thus,

AB = AC/SinB * SinC

= 1523/Sin109° * Sin39°
AB ≈ 1,014m

Learn more about the Sine Theorem at;
brainly.com/question/27174058
#SPJ1

You might be interested in

4 cos²x – 1=0<br><br> What is the solution?

andreev551 [17]

Answer:

$x=\frac{\pi }{3}+2\pi n, n\in \mathbb{Z}$

$\:x=\frac{5\pi }{3}+2\pi n, n \in \mathbb{Z}$

$x=\frac{2\pi }{3}+2\pi n, n\in \mathbb{Z}$

$\:x=\frac{4\pi }{3}+2\pi n, n \in \mathbb{Z}$

or

$x=\frac{\pi}{3}+\pi n, n \in \mathbb{Z}$

$x=\frac{2\pi }{3}+\pi n, n\in \mathbb{Z}$

Step-by-step explanation:

$4\text{cos}^2(x)-1=0\\4\text{cos}^2(x)=1\\$

$cos(x)=\pm\sqrt{\frac{1}{4} }$

$cos(x)=\pm\frac{1}{2}$

So, when cos(x) is equal to

$\frac{1}{2} \text{ and } -\frac{1}{2}$ ?

For

$cos(x)=\frac{1}{2}$

We are talking about x = 60º and x = 300º, Quadrant I and IV, respectively. In radians:

$x=\frac{\pi }{3}+2\pi n, n\in \mathbb{Z}$

$\:x=\frac{5\pi }{3}+2\pi n, n \in \mathbb{Z}$

or

$x=\frac{\pi}{3}+\pi n, n \in \mathbb{Z}$

For

$cos(x)=-\frac{1}{2}$

We are talking about x = 120º and x = 240º, Quadrant II and III, respectively. In radians:

$x=\frac{2\pi }{3}+2\pi n, n\in \mathbb{Z}$

$\:x=\frac{4\pi }{3}+2\pi n, n \in \mathbb{Z}$

or

$x=\frac{2\pi }{3}+\pi n, n\in \mathbb{Z}$

6 0

3 years ago

Simplify <br> 1+sinx/cosx+cosx/1+sinx

Dmitry [639]

$\frac{1 + sin(x)}{cos(x)} + \frac{cos(x)}{1 + sin(x)}$
$\frac{[1 + sin(x)][1 +sin(x)]}{cos(x)[1 + sin(x)]} + \frac{cos(x)[cos(x)]}{cos(x)[1 + sin(x)]}$
$\frac{1 + 2sin(x) + sin^{2}(x)}{cos(x)[1 + sin(x)]} + \frac{cos^{2}(x)}{cos(x)[1 + sin(x)]}$
$\frac{1 + 2sin(x) + sin^{2}(x) + cos^{2}(x)}{cos(x)[1 + sin(x)]}$
$\frac{1 + 2sin(x) + 1}{cos(x)[1 + sin(x)]}$
$\frac{1 + 1 + 2sin(x)}{cos(x)[1 + sin(x)]}$
$\frac{2 + 2sin(x)}{cos(x)[1 + sin(x)]}$
$\frac{2[1 + sin(x)]}{cos(x)[1 + sin(x)]}$
$\frac{2}{cos(x)}$
$2sec(x)$

6 0

3 years ago

In a random sample of 75 individuals, it was found that 52 of them prefer coffee to tea. What is the margin of error for the tru

Ugo [173]

0.106 is the answer

letters till 20 characters

4 0

4 years ago

A shipping tube is shaped like a triangular prism. The bases are equilateral triangles with edges of 5 inches and a height of 4.

zimovet [89]

Answer:

there is the thing you need to answer the question right

Step-by-step explanation:

4 0

3 years ago

The mean of 4 numbers is 21. calculate the sum of the 4 numbers

Ugo [173]

Answer:

84

Step-by-step explanation:

The mean is calculated as

mean = $\frac{sum}{count}$ , then

$\frac{sum}{4}$ = 21 ( multiply both sides by 4 )

sum = 84

8 0

3 years ago