Question

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.​

Answer 1

19.8 cm

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