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mariarad [96]
2 years ago
9

Find the length of the third side. If necessary, round to the nearest tenth. 30 18

Mathematics
1 answer:
grigory [225]2 years ago
8 0

Answer:

24

Step-by-step explanation:

use Pythagoras theorem

a^2 + b^2 = c^2

18^2+b^2=30^2

b^2 = 30^2 - 18^2

b = √576 =24

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A petrol kiosk p is 12 km due north of another petrol kiosk q. The bearing of a police station r from p is 135 degree and that f
tiny-mole [99]

Answer:

Distance between P and R is 40.15 km.

Step-by-step explanation:

From the picture attached,

Petrol kiosk P is 12 km due North of another petrol kiosk Q.

Bearing of a police station R is 135° from P and 120° from Q.

m∠QPR = 180° - 135° = 45°

m∠PQR = 120°

m∠PRQ = 180° - (m∠QPR +m∠PQR)

             = 180° - (45° + 120°)

             = 180° - 165°

             = 15°

Now we apply sine rule in ΔPQR to measure the distance between P and R.

\frac{\text{sin}(\angle QPR)}{\text{QR}}= \frac{\text{sin}(\angle PQR)}{\text{PR}}=\frac{\text{sin}\angle PRQ}{\text{PQ}}

\frac{\text{sin}(45)}{\text{QR}}= \frac{\text{sin}(120)}{\text{PR}}=\frac{\text{sin}(15)}{\text{12}}

\frac{\text{sin}(120)}{\text{PR}}=\frac{\text{sin}(15)}{\text{12}}

PR = \frac{12\text{sin}(120)}{\text{sin}(15)}

PR = 40.15 km

Therefore, distance between P and R is 40.15 km.

8 0
3 years ago
Please help please i really need help
vodomira [7]

Answer:

78

Step-by-step explanation:

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8 0
3 years ago
A bicycle wheel has a radius of 13 inches. What is the distance the bicycle will travel after 30 revolutions of the wheel? Use 3
SpyIntel [72]
Radius = 13 inches

Circumference of wheel = 1 revolution
2πr = 2 x 3.14 x 13 = 81.64 inches

1 revolution = 81.64 inches
30 revolutions = 2449.2inches
7 0
3 years ago
The diameter of a circle is 5 inches <br> find the length of its raidius
BARSIC [14]

Answer:

2.5 inches

Step-by-step explanation:

the radius is half diameter

6 0
3 years ago
Find the quotient of `(2i(4+5i)(4-5i))/(4+i)`, and express it in the simplest form.
DIA [1.3K]

Answer:

(328i + 82)  /  17

Step-by-step explanation:

`(2i(4+5i)(4-5i))/(4+i)

= (2i(16 - 25i^2)) / (4 + i)

= (2i( 16 + 25) )) / (4 + 1)        [Note:- i^2 = -1]

=  82i / (4 + i)

= 82i(4 - i) / (4 + i)(4 - 1)

= 328i  + 82 /   (16 - i^2)

= (328i + 82)  /  17

5 0
4 years ago
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