Questions: UNIT 4 LESSON 8 Inverse Trigonometry Solving Right Triangles

Solution Steps

It seems like the question is not fully clear or complete. However, based on the title "Inverse Trigonometry" and "Solving Right Triangles," I can provide a general approach to solving a right triangle using inverse trigonometric functions.

1. Identify the given sides or angles of the right triangle.
2. Use inverse trigonometric functions (like arcsin, arccos, arctan) to find the unknown angles.
3. Use the Pythagorean theorem to find the unknown side if needed.

We are given the sides of a right triangle:

• \( a = 3 \)
• \( b = 4 \)
• \( c = 5 \)

Using the inverse tangent function, we calculate the angles:

• \( \angle A = \arctan\left(\frac{a}{b}\right) = \arctan\left(\frac{3}{4}\right) \approx 36.87^\circ \)
• \( \angle B = \arctan\left(\frac{b}{a}\right) = \arctan\left(\frac{4}{3}\right) \approx 53.13^\circ \)

The third angle in a right triangle is always \( 90^\circ \):

• \( \angle C = 90^\circ \)

Final Answer