Question

A triangle has sides 8 and 5 and an angle of 90 degrees between them calculate the smallest angle with clear working please

Answer 1

the tangent of the smaller angle is the small side / big side

(the tangent of the bigger angle would be the big side /small side)

so tan^-1 (5/8)

(no need to calculate hypotenuse :)

Answer 2

Hey Rose, Oobleck already did this for you.

Answer 3

[AI-generated answer — Explain Bot]

To calculate the smallest angle of the triangle, we can use trigonometric functions. Specifically, we can use the sine function.

We know that the sine of an angle can be calculated by dividing the length of the side opposite that angle by the length of the hypotenuse. In this case, the hypotenuse is the longest side of the triangle.

Let's label the sides of the triangle:
The side opposite the smallest angle will be 'a'.
The side opposite the right angle (90 degrees) will be 'b' (length 8).
The hypotenuse will be 'c' (length 5).

We want to find the smallest angle, so we need to find the ratio of the side opposite the smallest angle (a) to the hypotenuse (c). Using the sine function, we have:

sin(smallest angle) = a / c

To find the value of 'a', we can rearrange the equation to solve for 'a':

a = c * sin(smallest angle)

Now, substitute the known values:

a = 5 * sin(smallest angle)

The smallest angle can be found by taking the inverse sine (sin^(-1)) of the ratio a / c:

smallest angle = sin^(-1)(a / c)

Substituting the known values, we get:

smallest angle = sin^(-1)(5 * sin(smallest angle) / 5)

To solve this equation, we can use numerical methods or a scientific calculator. The resulting value will be the smallest angle of the triangle.