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Answer:
a) base: 29.4377 cm
b) hypotenuse: 30.7827 cm
c) area: 132.470 cm²
d) perimeter: 69.2204 cm
Step-by-step explanation:
a) The mnemonic SOH CAH TOA reminds you that ...
Tan = Opposite/Adjacent
tan(17°) = (9 cm)/base
base = (9 cm)/tan(17°) = 29.4377 cm
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b) The sine relation could be used in the same way to find the hypotenuse:
hypotenuse = (9 cm)/sin(17°) ≈ 30.7827 cm
However, we're instructed to use the Pythagorean theorem. So, we have ...
hypotenuse = √(base² +(9 cm)²) ≈ √(886.577 +81) cm ≈ 30.7827 cm
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c) The area is half the product of the base and height:
A = 1/2bh
A = (1/2)(29.4377 cm)(9 cm) ≈ 132.470 cm²
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d) The perimeter is the sum of side lengths:
P = base + hypotenuse + height
P = (29.4377 +30.7827 +9) cm = 69.2204 cm
