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 in Triangle 2, we can use the Law of Sines.

First, calculate the angle at vertex D:

180° - 54° - 75° = 51°

Now, set up the Law of Sines equation for Triangle 2:

sin D / x = sin E / 45

Plug in the values we know:

sin 51° / x = sin 54° / 45

Now, solve for x:

x = 45 * sin 51° / sin 54°

x ≈ 41.5

Therefore, x is approximately 41.5.

Answer 2

Can you explain this answer?

Answer 3

Of course! To solve for x in Triangle 2, we used the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides and angles in a triangle.

In this case, we set up the Law of Sines equation by comparing the ratio of the sine of angle D to the length of side x with the ratio of the sine of angle E to the length of side 45. This gives us:

sin D / x = sin E / 45

We know the values of the angles in Triangle 2:

Angle D = 51°, Angle E = 54°

Then, we substitute these values into the equation and solve for x:

sin 51° / x = sin 54° / 45

x = 45 * sin 51° / sin 54°

By using trigonometric functions to calculate the sine of angles 51° and 54°, we can determine that x is approximately 41.5. This means that the length of side x in Triangle 2 is about 41.5.