Find the area of the triangle
1 answer:
You might be interested in
When given an angle, the side opposite the angle, and another side, you have to determine how many triangles are possible or if it is not possible.
Begin with when a triangle cannot exist:
1.) measure of non-inclusive angle is less than 90° and side opposite the angle < (other side)×sin(angle measure)
2.) measure of non-inclusive angle is ≥ 90° and side opposite the angle < other side
Next determine if two triangles exist:
Only if the measure of angle is less than 90° and
(other side)×sin(non-inclusive angle measure) < opposite side < other side
Otherwise 1 triangle exist...
HERE IS WHAT YOUR PROBLEM HAS:
Non-inclusive angle measure = 22° which is < 90°
Opposite side = 13
Other side = 18.1
(other side)×sin(non-inclusive angle measure) =(18.1)×sin(22°) ≈ 6.78
So how many triangles?
6.78 < 13 < 18.1 so 2 triangles exist
Now let's find them... find angle B with law of sines
Put the following in your calculator:
This gives you the first angle B value and if you subtract it from 180 you get the other angle B value
To find the angle C for the first triangle 180 - (sum of angle A and first angle B)
Then use the law of sines to find side c for first triangle.
To find the angle C for the 2nd triangle 180 - (sum of angle A and 2nd angle B)
Then use the law of sines to find side c for 2nd triangle.
Sorry, I didn't do the calculations because my calculator is dead.
Begin with when a triangle cannot exist:
1.) measure of non-inclusive angle is less than 90° and side opposite the angle < (other side)×sin(angle measure)
2.) measure of non-inclusive angle is ≥ 90° and side opposite the angle < other side
Next determine if two triangles exist:
Only if the measure of angle is less than 90° and
(other side)×sin(non-inclusive angle measure) < opposite side < other side
Otherwise 1 triangle exist...
HERE IS WHAT YOUR PROBLEM HAS:
Non-inclusive angle measure = 22° which is < 90°
Opposite side = 13
Other side = 18.1
(other side)×sin(non-inclusive angle measure) =(18.1)×sin(22°) ≈ 6.78
So how many triangles?
6.78 < 13 < 18.1 so 2 triangles exist
Now let's find them... find angle B with law of sines
Put the following in your calculator:
This gives you the first angle B value and if you subtract it from 180 you get the other angle B value
To find the angle C for the first triangle 180 - (sum of angle A and first angle B)
Then use the law of sines to find side c for first triangle.
To find the angle C for the 2nd triangle 180 - (sum of angle A and 2nd angle B)
Then use the law of sines to find side c for 2nd triangle.
Sorry, I didn't do the calculations because my calculator is dead.
<h3>Answer: 144</h3><h3>Step-by-step explanation:</h3><h3 />
Since, the first 9 multiple of 4 starts from 0 are,
0, 4, 8, 12, 16, 20, ................
Which is an AP,
Having the first term,
And, the successive difference, d = 4,
Since, the sum of the n term of an AP,
Hence the sum of 9 term of the above AP,