a triangle has sides 8cm and 5cm and angle 90 degree between them.calculate also the smallest angle of the triangle.
You have two legs of a right triangle.
So, you want x such that
tan x = 5/8
30°
To calculate the smallest angle of the triangle, we can use the trigonometric relationship between the sides and angles of a right triangle.
Given:
Side a = 8 cm
Side b = 5 cm
Angle C (between sides a and b) = 90 degrees
We'll use the trigonometric function sine (sin) to find the smallest angle of the triangle.
Step 1: Calculate the hypotenuse (side c) of the triangle using the Pythagorean theorem.
c^2 = a^2 + b^2
c^2 = 8^2 + 5^2
c^2 = 64 + 25
c^2 = 89
c = sqrt(89) ≈ 9.43 cm
Step 2: Use the sine function to find the smallest angle.
sin(A) = opposite / hypotenuse
sin(A) = a / c
sin(A) = 8 / 9.43
A = arcsin(8 / 9.43)
A ≈ 53.13 degrees
So, the smallest angle of the triangle is approximately 53.13 degrees.