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B
ABC is a right-angled triangle.
AC = 16 cm
Angle C = 90°
А.
size of angle B : size of angle A = 3:2
С
16 cm
Work out the length of AB.
Give your answer correct to 3 significant figures.​

BABC is a rightangled triangleAC 16 cmAngle C 90Аsize of angle B size of angle A 32С16 cmWork out the length of ABGive your answer correct to 3 significant figu class=

Respuesta :

sqdancefan

Answer:

  19.8 cm

Step-by-step explanation:

Angle B is the complement of angle A, so we have this relation for the angles:

  B/A = 3/2 = (90°-A)/A

  2(90° -A) = 3A . . . . . cross multiply

  180° = 5A . . . . . . . . . eliminate parentheses, add 2A

  36° = A . . . . . . . . . . . divide by 5

The relations expressed by the mnemonic SOH CAH TOA remind you that ...

  Cos = Adjacent/Hypotenuse

  cos(A) = AC/AB

  AB = AC/cos(A) = (16 cm)/cos(36°)

  AB ≈ 19.8 cm

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