The problem above uses a combination of sine and cosine law of triangle to solve for the m∠B.
Given:
<span>m∠A = 60°, b = 9 and c = 6
Cosine Law:
a^2=b^2+c^2-2bccosA
a^2=(9)^2+(6)^2-2(9)(6)cos(60)
a^2=81+36-54
a^2= 63
a=</span>
Sine Law
sin B= 9/
sin 60
sin B= 0.98198
B= sin ^-1 (0.98198) = 79.10
Therefore, m∠B is equal to 79.10
<u>Answer:</u>
x = 5.67
<u>Step-by-step explanation:</u>
We are given a right angled triangle with a length of the hypotenuse 8 with the remaining two sides (base and perpendicular) that are equal to each other.
Assuming the two equal legs of this right angled triangle to be x, we can use the Pythagoras Theorem to find the value of x.
Taking square root at both the sides to get:
Therefore, x = 5.67.
Answer:
$25,740
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 5%/100 = 0.05 per year,
then, solving our equation
I = 23400 × 0.05 × 2 = 2340
I = $ 2,340.00
The simple interest accumulated
on a principal of $ 23,400.00
at a rate of 5% per year
for 2 years is $ 2,340.00.
Answer:
The equations that represent the equation of the line are:
y = -2x + 16 ⇒ A
2x + y = 16 ⇒ D
y - 6 = -2(x - 5) ⇒ E
Step-by-step explanation:
The slope intercept form of the linear equation is y = m x + b, where
- m is the slope of the line
- b is the y-intercept (y at x = 0)
The formula of the slope is 
∵ The line is passing through points (5 , 6) and (4 , 8)
∴ 
= 5 and 
= 4
∴ 
= 6 and 
= 8
- Substitute them in the formula of the slope to find it
∵ 
∴ m = -2
- Substitute it in the form of the equation
∴ y = -2 x + b
- To find b substitute x and y in the equation by the coordinates
of any point in the line
∵ x = 5 and y = 6
∴ 6 = -2(5) + b
∴ 6 = -10 + b
- Add 10 to both sides
∴ 16 = b
∴ y = -2 x + 16
∴ The equation of the line is y = -2x + 16
∴ A represents the equation of the line
∵ 2x + y = 16
- Subtract 2x from both sides
∴ y = -2x + 16
∴ D represents the equation of the line
∵ y - 6 = -2(x - 5)
∴ y - 6 = -2x + 10
- Add 6 to both sides
∴ y = -2x + 16
∴ E represents the equation of the line
The equations that represent the equation of the line are:
y = -2x + 16 ⇒ A
2x + y = 16 ⇒ D
y - 6 = -2(x - 5) ⇒ E
