A triangle has sides 8 cm and 5 cm and an angle of 90 degrees between them. Calculate the smallest angle between them.
Well it is a right-angled triangle, so
tanØ = 5/8
Ø = appr 32°
( the 3rd angle would be 58° )
Answer:
tanØ = ⅝
= 0.625
Ø = 32° using the four figure table.
The Smallest angle will be:
90-32 = Δ?
= 58°
thank you Reiny
To calculate the smallest angle between the sides of a triangle, we can use trigonometric functions. In this case, since we know the lengths of two sides and the angle between them, we can use the sine function.
The smallest angle, let's call it θ, can be found using the formula:
sin(θ) = opposite/hypotenuse
In this case, the side opposite the angle (θ) is 8 cm, and the hypotenuse is the side opposite the right angle, which is 5 cm. So we have:
sin(θ) = 8/5
To find the value of θ, we need to take the inverse sine (also known as arcsine) of 8/5. We can use a calculator or trigonometric tables to find this value.
Using a calculator, we find that the inverse sine of 8/5 is approximately 56.44 degrees.
Therefore, the smallest angle between the sides is approximately 56.44 degrees.