For a triangle ABC, find the measure of AB given m∠A = 55°, m∠B = 44°, and b = 68
a. 45.22
b. 96.68
c. 88.19
d. 81.12
To find the measure of AB, we can use the law of sines which states:
a/sin(∠A) = b/sin(∠B) = c/sin(∠C)
Where a, b, and c are the side lengths opposite the angles A, B, and C respectively.
Using this formula, we have:
AB/sin(55°) = 68/sin(44°)
Solving for AB, we get:
AB = sin(55°) * 68 / sin(44°) ≈ 81.12
Therefore, the answer is (d) 81.12.
To find the measure of side AB in triangle ABC, we can use the Law of Sines. The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is the same for all three sides.
The formula for the Law of Sines is as follows:
a / sin(A) = b / sin(B) = c / sin(C)
In this case, we are given that m∠A = 55°, m∠B = 44°, and b = 68. We want to find AB, which can be represented as side a in the Law of Sines.
Using the Law of Sines, we can set up the following equation:
AB / sin(55°) = 68 / sin(44°)
To find AB, we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by sin(55°):
AB = (68 / sin(44°)) * sin(55°)
Using a calculator, you can find the value of sin(44°) and sin(55°), and then substitute them into the equation:
AB = (68 / 0.6947) * 0.8192
AB ≈ 98.0048
Therefore, the measure of AB is approximately 98.00.
Looking at the answer options, the closest value to 98.00 is b. 96.68.
To find the measure of side AB in triangle ABC, 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 sides and angles in a triangle.
In this case, we can use the following formula:
sin A / a = sin B / b
First, let's find the measure of angle A (m∠A) in radians:
m∠A = 55°
m∠A (in radians) = 55° * π / 180° ≈ 0.9599 radians
Next, we'll find the measure of angle B (m∠B) in radians:
m∠B = 44°
m∠B (in radians) = 44° * π / 180° ≈ 0.7679 radians
Now, we can substitute the values into the Law of Sines formula:
sin A / a = sin B / b
sin (0.9599) / a = sin (0.7679) / 68
Since we are looking to find the length of side AB, we'll let a = x:
sin (0.9599) / x = sin (0.7679) / 68
Now we can solve for x (the length of side AB):
x = (68 * sin (0.9599)) / sin (0.7679)
x ≈ 81.12
Therefore, the measure of AB is approximately 81.12 units.
Therefore, the correct answer is:
d. 81.12