In triangle ABC a equals to 38 degree 18 seconds a=252m,b=198m,solve the triangle completely
Solution pls.
Where is the solution I don't understand.
I dont understand
To solve the triangle completely, we need to find the remaining angles and sides of triangle ABC.
Let's tackle it step by step:
1. Given side lengths:
- Side a = 252m
- Side b = 198m
2. Angle A:
- Angle A is given to be 38 degrees and 18 seconds.
- 18 seconds can be converted to degrees by dividing it by 60.
- 18 seconds / 60 = 0.3 degrees
- So, Angle A = 38.3 degrees
3. To find Angle B:
- We can use the Law of Sines, which states: a/sin(A) = b/sin(B) = c/sin(C).
- Rearranging the formula, we have sin(B) = b * sin(A) / a
- sin(B) = 198 * sin(38.3) / 252
- Using a calculator, sin(B) ≈ 0.3553
- To find Angle B, take the inverse sine (sin^-1) of 0.3553:
- Angle B ≈ 21.5 degrees
4. To find Angle C:
- Since the sum of angles in a triangle is always 180 degrees, we can calculate Angle C:
- Angle C = 180 - Angle A - Angle B
- Angle C = 180 - 38.3 - 21.5
- Angle C ≈ 120.2 degrees
5. To find the remaining side length c:
- We can use the Law of Sines again: a/sin(A) = b/sin(B) = c/sin(C).
- Rearranging the formula, we have c = a * sin(C) / sin(A)
- c = 252 * sin(120.2) / sin(38.3)
- Using a calculator, c ≈ 404.3m
So, the missing angles are Angle B ≈ 21.5 degrees and Angle C ≈ 120.2 degrees, and the missing side length is c ≈ 404.3m.
sinB/b = sinA/a
Now you know that A+B+C = 180
so use the law of sines again to get c.
Or use the law of cosines, since you know a,b,C