solve for x. round your answer to the nearest tenth if necessary.
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.
To solve for x in Triangle 2, we can use the Law of Sines which states that the ratio of the length of a side to the sine of its opposite angle is constant for all three sides of a triangle.
In Triangle 1:
sin A / a = sin B / b = sin C / c
sin 51° / 16 = sin 54° / 17
0.788 / 16 = 0.809 / 17
0.04925 = 0.04759
a = 16, b = 17, and c = unknown
Let's calculate angle E for Triangle 2:
angle E = 180 - (54 + 75)
angle E = 51°
Now we can set up the Law of Sines for Triangle 2:
sin D / 45 = sin E / x
sin 51° / 45 = sin 51° / x
0.788 / 45 = 0.788 / x
0.0175 = 0.0224
x = 45 * 0.0175 / 0.0224
x = 35.15625
Therefore, x is approximately 35.2 to the nearest tenth.