steve, do you solve this cause i don't know how and i don't get it :
b/sin49° = c/sin115° = 10/sin16°
Notice one of the fractions is a constant, so use
b/sin49 = 10/sin16
b = 10sin49/sin16
you should get appr 27.38
then
c/sin115 = 10/sin16
c = 10sin115/sin16 = 32.88
To solve this problem, we can use the Law of Sines. The Law of Sines states that for any triangle with sides a, b, and c opposite angles A, B, and C, the following relationship holds:
a/sinA = b/sinB = c/sinC
In this case, we are given:
b/sin49° = c/sin115° = 10/sin16°
1. We will start by using the first equality: b/sin49° = 10/sin16°
To solve for b, we can cross-multiply:
b * sin16° = 10 * sin49°
Now, divide both sides of the equation by sin16°:
b = (10 * sin49°) / sin16°
2. Next, let's solve the second equality: c/sin115° = 10/sin16°
To solve for c, cross-multiply:
c * sin16° = 10 * sin115°
Divide both sides of the equation by sin16°:
c = (10 * sin115°) / sin16°
Therefore, the solutions for b and c (rounded to a reasonable number of decimal places) are:
b ≈ 26.91
c ≈ 31.76
So, the approximate values for b and c are 26.91 and 31.76, respectively.