Title: Analyzing a Right Triangle### Problem Statement:Given a right triangle ABC with the following dimensions:- Side AC = 7 units- Side BC = 6 units### Required:Determine the following:1. The measure of angle ∠B.2. The measure of angle ∠A.3. The length of side AB.### Diagram:The diagram depicts a right triangle labelled ABC. The right angle is at vertex C. The lengths of sides AC and BC are 7 units and 6 units, respectively.### Solution:1. **Calculate the Hypotenuse (AB):** Using the Pythagorean theorem for right-angled triangles: \[ AB^2 = AC^2 + BC^2 \] Substituting the known values: \[ AB^2 = 7^2 + 6^2 \\ AB^2 = 49 + 36 \\ AB^2 = 85 \\ AB = \sqrt{85} \\ AB \approx 9.22 \text{ units} \\ \]2. **Measure of Angle ∠B:** Since we know the values of the opposite side (BC) and the adjacent side (AC), we can use the tangent function: \[ \tan(B) = \frac{\text{opposite}}{\text{adjacent}} \\ \tan(B) = \frac{6}{7} \] Using an inverse tangent function (arctan) to find the measure of angle B: \[ B = \arctan\left(\frac{6}{7}\right) \\ B \approx 40.60^\circ \]3. **Measure of Angle ∠A:** Since the sum of the angles in any triangle is 180 degrees and one angle is 90 degrees: \[ A + B = 90^\circ \\ A = 90^\circ - B \\ A = 90^\circ - 40.60^\circ \\ A \approx 49.40^\circ \]### Conclusion:- ∠B ≈ 40.60°- ∠A ≈ 49.40°- The length of side AB ≈ 9.22 units.

Name: Title: Analyzing a Right Triangle### Problem Statement:Given a right
Uploaded: 2024-03-20T06:47:08.000Z
Channel: Bartleby
Description: Title: Analyzing a Right Triangle### Problem Statement:Given a right triangle ABC with the following dimensions:- Side AC = 7 units- Side BC = 6 units### Required:Determine the following:1. The measure of angle ∠B.2. The measure of angle ∠A.3. The l