This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Alright gurlll_zelight! — let's do this. Part 1: Calculate w, x, y, z to 2 significant figures. For triangle a): Step 1: Find w. We use the tangent function, as w is the adjacent side and 10 is the opposite side to the 78^ angle. () = oppositeadjacent (78^) = (10)/(w) w = (10)/((78^)) w ≈ (10)/(4.7046) w ≈ 2.1255 Rounding to 2 significant figures: w ≈ 2.1 Step 2: Find x. We use the sine function, as 10 is the opposite side and x is the hypotenuse to the 78^ angle. () = oppositehypotenuse (78^) = (10)/(x) x = (10)/((78^)) x ≈ (10)/(0.9781) x ≈ 10.2239 Rounding to 2 significant figures: x ≈ 10 For triangle b): Step 3: Find z. We use the sine function, as z is the opposite side and 7 is the hypotenuse to the 22^ angle. () = oppositehypotenuse (22^) = (z)/(7) z = 7 × (22^) z ≈ 7 × 0.3746 z ≈ 2.6222 Rounding to 2 significant figures: z ≈ 2.6 Step 4: Find y. We use the cosine function, as y is the adjacent side and 7 is the hypotenuse to the 22^ angle. () = adjacenthypotenuse (22^) = (y)/(7) y = 7 × (22^) y ≈ 7 × 0.9272 y ≈ 6.4904 Rounding to 2 significant figures: y ≈ 6.5 Part 2: If = 53^, what is ? Step 1: Use the complementary angle identity. The identity states that A = (90^ - A). Therefore, we can rewrite 53^ as (90^ - 53^). 53^ = (90^ - 53^) 53^ = (37^) Step 2: Solve for . Given = 53^, substitute the result from Step 1: = 37^ Therefore, = 37^ Send me the next one 📸