A triangle has side's 8cm and 15cm and an angle of 90 degree between them calculate the smallest angle of the triangle with working
the smallest angle is opposite the shortest side
... in this case ... 8 cm
tan(Θ) = 8 / 15
what is the answer am so confuesed
In a right triangle, the smallest angle is always opposite the smallest side. So, in this case, the smallest angle will be opposite the side of length 8cm.
To find the smallest angle, we can use trigonometric ratios. Specifically, we can use the sine ratio.
The sine ratio is defined as follows:
sin(angle) = opposite/hypotenuse
In this case, the opposite side is 8cm and the hypotenuse is 15cm.
sin(angle) = 8/15
To find the angle, we need to take the inverse sine (also known as arcsine) of the ratio. This can be done using a scientific calculator or by using a mathematical software.
Using a calculator, we can find:
angle = arcsin(8/15) = 29.118 degrees (rounded to three decimal places)
Therefore, the smallest angle of the triangle is approximately 29.118 degrees.
To calculate the smallest angle of a triangle, you can use the law of cosines. Let's label the sides of the triangle: the side opposite the 90-degree angle as "c," the side of length 8cm as "a," and the side of length 15cm as "b." The law of cosines states that:
c^2 = a^2 + b^2 - 2ab * cos(C),
where C is the angle opposite side c. In this case, since we want to find the smallest angle, we are interested in angle C.
First, let's calculate the value of c:
c^2 = a^2 + b^2 - 2ab * cos(C)
c^2 = 8^2 + 15^2 - 2 * 8 * 15 * cos(90 degrees)
Now, let's calculate the cosine of 90 degrees:
cos(90 degrees) = 0
Substituting this value back into the equation:
c^2 = 8^2 + 15^2 - 2 * 8 * 15 * 0
c^2 = 64 + 225 - 0
c^2 = 289
Taking the square root of both sides:
c = √(289)
c = 17
Now, we have the value of c. We can substitute it back into the equation to find the angle C:
17^2 = 8^2 + 15^2 - 2 * 8 * 15 * cos(C)
289 = 64 + 225 - 0
289 = 289
Therefore, the smallest angle of the triangle is 90 degrees.
I hope this explanation helps! Let me know if you have any further questions.