Question

A triangle has sides 8 cm and 5 cm and an angle of 90° between them. Calculate the smallest angle of the triangle. ​

Answer 1

Answer: The smallest angle of the triangle is 32°

Explanation:

Given:

one side of the triangle= 8 cm

The other side of the triangle = 5 cm

Angle between AB and BC = 90°

⇒ ∠ABC = 90°

ΔABC is a right angled triangle

Use trigonometric function: For X

tanx= AB/CB

tanx= 8/5

x=tan-1 (8/5)

x= 58°

Use trigonometric function: For Y

tany= BC/AB

tany=5/8

y=tan-1 (5/8)

y = 32°

Making 32° be the smallest angle of the triangle

Answer 2

Explanation:

let the smallest angle = x

tan x = 5/8

x = arctan 5/8

x = 32°