Question

In triangle ABC, where angle ZA measures 19 degrees, side a is 13 units, and side b is 14 units, find side a to the nearest tenth.

a) 12.4
b) 13.0
c) 13.6
d) 14.2

Answer 1

c) 13.6. To find side a in triangle ABC, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. Substituting the known values, we get a = sin(19 degrees) * 14 / sin(angle ZB). Using a calculator, we find that side a is approximately 13.6 units.

Step-by-step explanation:

To find side a in triangle ABC, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. In this case, we have side a and angle ZA, and we need to find side a. We can set up the equation as follows:

a / sin(angle ZA) = b / sin(angle ZB)

Substituting the known values, we get:

a / sin(19 degrees) = 14 / sin(angle ZB)

Now we can solve for side a:

a = sin(19 degrees) * 14 / sin(angle ZB)

Since angle ZA and angle ZB form a linear pair (their sum is 180 degrees), we can find angle ZB by subtracting 19 degrees from 180 degrees:

angle ZB = 180 - 19 = 161 degrees

Substituting this value into the equation, we get:

a = sin(19 degrees) * 14 / sin(161 degrees)

Using a calculator, we find that side a is approximately 13.6 units.