based on the measurements shown on abc ab must be

based on the measurements shown on triangle ABC , AB must be ?

In triangle ABC, we are tasked with determining the length of side AB based on the given angle measurements and side lengths. Specifically, we know that angle A = 47°, angle B = 68°, and side BC = 10 feet, while side AC is 7 feet. Using these values, we can apply the Law of Sines to calculate the length of side AB.

Explanation
The Law of Sines states that for any triangle:

$$\frac{AB}{\sin(C)} = \frac{AC}{\sin(B)} = \frac{BC}{\sin(A)}$$

In this case, we can use the Law of Sines to solve for side AB. First, we need to find angle C. Since the sum of the angles in a triangle is always 180°, we can calculate angle C as:

$$\text{Angle C} = 180° - 47° - 68° = 65°$$

Now, we apply the Law of Sines:

$$\frac{AB}{\sin(65°)} = \frac{7}{\sin(68°)}$$

Solving for AB:

$$AB = \frac{7 \times \sin(65°)}{\sin(68°)}$$

By calculating the sine values and performing the division:

$$AB ≈ \frac{7 \times 0.9063}{0.9271} ≈ 6.83 \text{ feet}$$

Answer
Based on the calculations, the length of side AB is approximately 6.83 feet. Therefore, the correct answer is:

• Less than 7 feet

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