Questions: Angle A= □ Angle B= □

Angle A= □
Angle B= □
Transcript text: Angle $A=$ $\square$ Angle $B=$ $\square$
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Solution

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Solution Steps

Step 1: Identify the Right Triangle

The given triangle is a right triangle with sides 48 (adjacent to angle A) and 36 (opposite to angle A).

Step 2: Use Trigonometric Ratios to Find Angle A

To find angle A, use the tangent function: \[ \tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{36}{48} = 0.75 \] \[ A = \tan^{-1}(0.75) \]

Step 3: Calculate Angle A

Using a calculator: \[ A \approx \tan^{-1}(0.75) \approx 36.87^\circ \]

Step 4: Calculate Angle B

Since the sum of angles in a triangle is 180 degrees and one angle is 90 degrees: \[ B = 90^\circ - A \] \[ B = 90^\circ - 36.87^\circ \approx 53.13^\circ \]

Final Answer

  • Angle A ≈ 36.87°
  • Angle B ≈ 53.13°
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