Question

What is the length of segment AC? Round your answer to the nearest hundredth.

triangles ABC and ABD in which the triangles share segment AB and angle B is a right angle, the measure of angle CAB is 34 degrees, the measure of angle BDA is 31 degrees, and the measure of segment AB is 3 units

2.49 units
3.62 units
4.48 units
5.36 units

Answer 1

To find the length of segment AC, we can use the Law of Sines to find the length of side BC and then use the Pythagorean Theorem to find the length of segment AC. The length of segment AC is approximately 3.62 units.

Step-by-step explanation:

To find the length of segment AC, we can use the Law of Sines. In triangle ABC, we have angle ACB as 90 degrees, angle CAB as 34 degrees, and side AB as 3 units.

First, let's find the length of side BC using the Law of Sines: sin(90)/BC = sin(34)/3.

Solving for BC, we get BC ≈ 1.82 units.

Now, to find the length of segment AC, we use the Pythagorean Theorem: AC^2 = AB^2 + BC^2.

Plugging in the values, we get AC^2 = 3^2 + 1.82^2.

Simplifying, we find AC ≈ 3.62 units. Therefore, the length of segment AC is approximately 3.62 units.