Calculate angle using arccos, arcsin, arctan

CONCEPTS

Angles in Right Triangles

• cos⁻¹ (b/c) = arcsin (b/c) = θ

• sin⁻¹ (a/c) = arcsin (a/c) = θ

• tan⁻¹ (b/a) = arctan (b/a) = θ

• Angle of inclination / ascent / elevation all mean the same thing. It is the angle between horizontal line & the slanted line or hypotenuse (angle C in the triangle above)

PRACTICE PROBLEMS

Question 1 Write expression to solve for θ (see picture below)?

-- Answer -- θ = sin⁻¹ (4/7)

Question 2 Write an expression to find the angle of elevation between the staircase & floor (see picture below)?

-- Answer -- sin⁻¹ (10 / 26)

Angle of elevation is between the horizontal and angled line, sin⁻¹ (opp / hyp) = sin⁻¹ (10/26)

ACT PRACTICE PROBLEMS