1. Given any triangle ABC with sides BC=a, AC=b and AB=c, the following are true :
i) the larger the angle, the larger the side in front of it, and the other way around as well. (Sine Law) Let a=20 in, then the largest angle is angle A.
ii) Given the measures of the sides of a triangle. Then the cosines of any of the angles can be found by the following formula:

2.

3. m(A) = Arccos(-0.641)≈130°,
4. Remark: We calculate Arccos with a scientific calculator or computer software unless it is one of the well known values, ex Arccos(0.5)=60°, Arccos(-0.5)=120° etc
Answer:
y= -5x +24
Step-by-step explanation:
<u>Slope-intercept form</u>
y= mx +c, where m is the slope and c is the y-intercept.
Given that the slope is -5, m= -5.
Substitute m= -5 into the equation:
y= -5x +c
To find the value of c, substitute a pair of coordinates that the line passes through into the equation:
When x= 3, y= 9,
9= -5(3) +c
9= -15 +c
c= 9 +15
c= 24
Thus, the equation of the line is y= -5x +24.
Answer:
Step-by-step explanation:
It 14
The value of a is 80
Step-by-step explanation:
The distance of a point
from the y-axis can be written as

because the x-coordinate of the y-axis is zero.
Similarly, the distance of a point
from the x-axis can be written as

Since the y-coordinate of the x-axis is zero.
In this problem:
- The distance of the point A (−30, −45) from the y-axis can be written as

- The distance of point B (a,a) from the x-axis can be written as

Since
.
We are told that 2/3 of the distance from the y-axis to point A (−30, −45) is equal to 1/4 of the distance from the x-axis to point B(a, a), which means

Therefore,

And solving for a,

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