calculate the values of a, A and C in ABC given that b=17.23cm, c=10.86cm and B= 10115degree
use the law of sines
sinC/c = sinB/b
Now you know B and C, so A is easy
Then use law of sines or law of cosines to get a
To calculate the values of a, A, and C in triangle ABC, we can use the Law of Sines:
a/sin A = b/sin B = c/sin C
Given that b = 17.23 cm and c = 10.86 cm, and B = 101.15 degrees, we can re-arrange the formula as follows:
a/sin A = 17.23/sin 101.15 = 10.86/sin C
First, let's calculate sin B, sin C, and sin A.
sin B = sin(101.15 degrees)
To find the value of sin B, you will need to use a calculator or lookup table. The sine function gives the ratio of the length of the side opposite the angle to the length of the hypotenuse.
sin B = 0.9786 (rounded to four decimal places)
Next, calculate sin C:
sin C = c/b = 10.86/17.23
sin C = 0.6300 (rounded to four decimal places)
Finally, calculate sin A:
sin A = a/b = 17.23/sin B
sin A = 17.23/0.9786
sin A = 17.6322 (rounded to four decimal places)
Now that we have sin A and sin C, we can calculate the values of A and C:
A = sin^(-1)(sin A)
This equation gives us the measure of angle A using the inverse sine function (sin^(-1)).
A = sin^(-1)(0.9979)
Using a calculator, we find that A = 82.36 degrees.
C = sin^(-1)(sin C)
Similarly, this equation gives us the measure of angle C.
C = sin^(-1)(0.6300)
C = 39.70 degrees.
So, the values of a, A, and C in triangle ABC, given that b = 17.23 cm, c = 10.86 cm, and B = 101.15 degrees, are:
a ≈ 17.6322 cm
A ≈ 82.36 degrees
C ≈ 39.70 degrees