a triangle has sides 8cm and 5cm and an angle of 90 between them. calculate the smallest angle of the triangle
What is the bigger angle then
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To calculate the smallest angle of a triangle with two known side lengths and an angle between them, you can use the law of cosines. This law states that in any triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of those sides multiplied by the cosine of the angle between them.
In this case, let's label the sides of the triangle as follows:
- The side opposite the 90-degree angle is the hypotenuse (H).
- The side of length 8 cm is labeled as side a.
- The side of length 5 cm is labeled as side b.
Using the law of cosines, we can set up the equation:
H^2 = a^2 + b^2 - 2ab * cos(C)
Substituting the given values into the equation:
H^2 = 8^2 + 5^2 - 2 * 8 * 5 * cos(90)
Simplifying the equation:
H^2 = 89
Taking the square root of both sides:
H = √89
Since the smallest angle in a right-angled triangle is always opposite the shortest side, and the side opposite the smallest angle is 5 cm, this means that the smallest angle is opposite side b, which is the side of length 5 cm.
tanTheta=5/8
theta= arcTan(5/8)