Answer:
10.8
Step-by-step explanation:
By sine rule:
![\frac{x}{ \sin 81 \degree} = \frac{7}{ \sin 40 \degree} \\ \\ x = \frac{7 \sin 81 \degree}{ \sin 40 \degree} \\ \\ x = \frac{7 \times0.9876883406 }{0.6427876097} \\ \\ x = \frac{6.91381838}{0.6427876097} \\ \\ x = 10.755992 \\ \\ x \approx 10.8](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7B%20%5Csin%2081%20%5Cdegree%7D%20%20%3D%20%20%5Cfrac%7B7%7D%7B%20%5Csin%2040%20%5Cdegree%7D%20%20%5C%5C%20%20%5C%5C%20x%20%3D%20%5Cfrac%7B7%20%5Csin%2081%20%5Cdegree%7D%7B%20%5Csin%2040%20%5Cdegree%7D%20%20%20%5C%5C%20%20%5C%5C%20x%20%3D%20%20%5Cfrac%7B7%20%5Ctimes0.9876883406%20%7D%7B0.6427876097%7D%20%20%5C%5C%20%20%5C%5C%20x%20%3D%20%20%5Cfrac%7B6.91381838%7D%7B0.6427876097%7D%20%20%5C%5C%20%20%5C%5C%20x%20%3D%2010.755992%20%5C%5C%20%20%5C%5C%20x%20%20%5Capprox%2010.8)
The answer is 46.
Since the sum of the interior angles of a triangle is always 180,
We can find out angle C by subtracting the other two angles
180-102-32=46
We can compare by converting Johnny's reading time into the same unit of Jacky's, hours.
There are 60 minutes in an hour, so use this:
![\frac{1}{3} * \frac{60}{1} = 20](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B3%7D%20%2A%20%20%5Cfrac%7B60%7D%7B1%7D%20%3D%2020)
15 < 20, so Johnny read faster. This is 5 pages faster per hour than Jacky.
Answer:
84.85cm
Step-by-step explanation:
Let the sides of the square be x
The perimeter of the square = 4x
Get x using the pythagoras theorem
x^2 + x^2 = 30^2
2x^2 = 900
x^2 = 450
x = 21.21cm
Perimeter of the plate = 4(21.21)
Perimeter of the plate = 84.85cm