Question

if the sides of a triangle are 3, 4, and 5, then, to the nearest degree, the measure of the smallest angle of the triangle is _____?

Answer 1

The measure of the smallest angle in a right triangle with sides 3, 4, and 5, is approximately 53 degrees.

Step-by-step explanation:

If the sides of a triangle are 3, 4, and 5, this is a right triangle, as these sides satisfy the Pythagorean theorem (32 + 42 = 52). The smallest angle in a right triangle is opposite the shortest side. We can use trigonometry to find this angle, specifically the function cosine.

Let's denote the smallest angle as θ, and we consider the sides 3 (adjacent to θ) and 5 (the hypotenuse). According to trigonometric definitions, cos(θ) = adjacent/hypotenuse = 3/5. By taking the inverse cosine, we can determine the measure of the smallest angle θ.

θ = cos-1(3/5) = 53.13° to the nearest hundredth of a degree. We round this to the nearest degree to get 53°, which is the measure of the smallest angle in the triangle.

Answer 2

4=5xsin
`\alpha`
4/5=sin
`\alpha`

`\alpha`=54 degrees
is 54,90,36