Question

Solve the triangle. Round your answer to the new nearest tenth

Answer 1

A = 44º

`b \approx 28.99`

`c \approx 40.31`

Explanation:

In this problem we are tasked with "solving the triangle," which means we need to solve for each of the triangle's non-given dimensions.

We can first solve for angle A, since we are given the other two interior angles of the triangle (90º and 46º), and we know that the measures of the interior angles of a triangle add to 180º.

A + 90º + 46º = 180º

A = 180º - 90º - 46º

A = 44º

Now that we have angle A, we can use the Law of Sines to solve for side length b.

`(a)/(\sin(A)) = (b)/(\sin(B))`

`(28)/(\sin(44\textdegree)) = (b)/(\sin(46\textdegree))`

`b = (28\sin(46\textdegree))/(\sin(44\textdegree))`

`b \approx 28.99`

Finally, we can solve for c using the Pythagorean Theorem.

a² + b² = c²

28² + 28.99² ≈ c²

`c \approx √(1624.70)`

`c \approx 40.31`