Someone please help me with this (look at the image above)

9514 1404 393

  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

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step-by-step explanation: