Answer:
1. cos = adjacent / hypotenuse
tan = opposite / adjacent
sin = opposite / hypotenuse
2. cos = adjacent / hypotenuse
cos(G) = 429/821 = 0.5225 ≈ 0.523
tan = opposite / adjacent
tan(G) = 700/429 = 1.6317 ≈ 1.632
sin = opposite / hypotenuse
sin(G) = 700/821 = 0.8526 ≈ 0.853
3. Part A:
sin(G) = opp / hyp = 420/427 = 0.9836 ≈ 0.984
Part B:
tan(Z) = opp / adj = 77 / 420 = 0.1833 ≈ 0.183
Part C:
cos(Z) = adj / hyp = 420 / 427 = 0.9836 ≈ 0.984
Part D:
sin(M) = opp / hyp = 427 / 427 = 1
Part E:
The sine value of any right angle is 1. The opposite side to the right angle is the hypotenuse.
Explanation:
1. Use "SohCahToa" to remember the equations.
S = o/h C = a/h T = o/a
"o" for opposite; "h" for hypotenuse; "a" for adjacent
"S" is sine; "C" is cosine; "T" is tangent.
2. Use the formulas for sin, cos and tan. Substitute the numbers for each side into the equations.
Since the values depend on ∠G, ∠G determines which side is opposite or adjacent. The adjacent side touches ∠G but the opposite side does not. The hypotenuse is the longest side.
3. Use the sin, cos and tan formulas from question 1. Which side is called opposite or adjacent depends on which angle (G, Z or M).
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