1. use the law of Sines to solve (if possible) the triangle for the value of c. A=27.5degrees, a=15cm, b=36.4cm
2. use the law of Sines to solve (if possible) the triangle for the value of c.
B=52degrees, a=8cm, b=12cm
How do I solve these type of problems?
apply the law of sines to get B or A.
recall that A+B+C = 180°
Then use the law of sines again.
To solve these problems, you can use the Law of Sines, which relates the sides of a triangle to the sines of its angles. The Law of Sines states:
a/sin(A) = b/sin(B) = c/sin(C)
To solve for the value of c, you can rearrange the equation to isolate c:
c = (a * sin(C)) / sin(A)
Now, let's solve the two given problems step by step.
1. Given A = 27.5 degrees, a = 15 cm, and b = 36.4 cm. To find the value of c, we'll substitute the given values into the equation:
c = (15 cm * sin(C)) / sin(27.5 degrees)
To find sin(C), we need to use the fact that the sum of the interior angles of a triangle is 180 degrees. Therefore:
C = 180 - A - B
C = 180 - 27.5 - B
Now, to find sin(C), you can use a scientific calculator or a trigonometric table. Substitute the value of C you calculated into the equation to solve for c.
2. Given B = 52 degrees, a = 8 cm, and b = 12 cm. Similarly, to find c, we'll use the law of sines:
c = (8 cm * sin(C)) / sin(52 degrees)
To find sin(C), we use the sum of interior angles:
C = 180 - A - B
C = 180 - A - 52
Now, you can solve for sin(C) and substitute the value of C into the equation to calculate c.
Remember, if you are using a calculator, make sure it is in the correct mode (either degrees or radians) to obtain accurate results.