Calculate the angles in the figure below.

Welcome back — been a while! Let's pick up where you left off. Here are the solutions to the problems: 1) Calculate the angles in the figure below. a) Calculate Step 1: Identify the known sides relative to angle . The side opposite is 3. The side adjacent to is 4. Step 2: Use the tangent function. () = oppositeadjacent () = (3)/(4) Step 3: Calculate . = ((3)/(4)) ≈ 36.87^ The angle is 36.87^. b) Calculate Step 1: Identify the known sides relative to angle . The side opposite is 2. The side adjacent to is 7. Step 2: Use the tangent function. () = oppositeadjacent () = (2)/(7) Step 3: Calculate . = ((2)/(7)) ≈ 15.95^ The angle is 15.95^. c) Calculate Step 1: Identify the known sides relative to angle . The side opposite is 4. The hypotenuse is 5. Step 2: Use the sine function. () = oppositehypotenuse () = (4)/(5) Step 3: Calculate . = ((4)/(5)) ≈ 53.13^ The angle is 53.13^. 2) Find the lettered sides in the figure below. a) Find x Step 1: Identify the known angle and sides relative to x. The angle is 30^. The side adjacent to 30^ is 4. The hypotenuse is x. Step 2: Use the cosine function. (30^) = adjacenthypotenuse (30^) = (4)/(x) Step 3: Solve for x. x = (4)/((30^)) x = (4)/(sqrt(3))2 x = (8)/(sqrt(3)) x = 8sqrt(3)3 x ≈ 4.62 The side length is 4.62. b) Find y Step 1: Identify the known angle and sides relative to y. The angle is 47^. The side opposite 47^ is y. The side adjacent to 47^ is 5. Step 2: Use the tangent function. (47^) = oppositeadjacent (47^) = (y)/(5) Step 3: Solve for y. y = 5 × (47^) y ≈ 5 × 1.0724 y ≈ 5.36 The side length is 5.36. c) Find z Step 1: Identify the known angle and sides relative to z. The angle is 52^. The side opposite 52^ is z. The hypotenuse is 7. Step 2: Use the sine function. (52^) = oppositehypotenuse (52^) = (z)/(7) Step 3: Solve for z. z = 7 × (52^) z ≈ 7 × 0.7880 z ≈ 5.52 The side length is 5.52. Send me the next one 📸