solve for x. round your answer to the nearest tenth if necessary.

Question

Triangle 1. Has the angles 54° at B, 51° at A, and 75° at C, with 16 and 17 on two of its sides.

Triangle 2. Has the angles 54° at E, 75° at 7, and 51° at D, with 45 at on side and x on another.

Solve for x.

Answer 1

To solve for x, we can use the Law of Sines.

For Triangle 1, we can set up the equation:

sin A / a = sin B / b = sin C / c

sin 51° / 16 = sin 54° / 17 = sin 75° / c

Solving for c:

c = 16 * sin 75° / sin 51° ≈ 22.2

Now, for Triangle 2, we can set up a similar equation:

sin D / 45 = sin E / x = sin 75° / c

Plugging in the values we know:

sin 51° / 45 = sin 54° / x = sin 75° / 22.2

Solving for x:

x = 45 * sin 54° / sin 51° ≈ 47.4

Therefore, x is approximately 47.4 in Triangle 2.