Question

How do i find m<d???

Answer 1

Using the tangent ratio, `tanD=2/5, D=arctan(2/5)approx25.8°`

Explanation:

We're given a right triangle with two known sides, and we're told to find an angle measure. Thus, we'll have no problem using the sine, cosine, and tangent trigonometric ratios.

For angle `D,` we know the measures of the sides opposite and adjacent to the angle.
The ratio which uses these two sides is the tangent ratio, as `tanA=(opposite)/(adjacent)` where `A` is some angle.

`tanD=2/5`

To find `D,` we take the arctangent of `2/5` using a calculator and round to one decimal place (nearest tenth):

`D=arctan(2/5)approx25.8°`

Answer 2

`\angleD = 21.8^o`

Explanation:

We are given a right triangle. Given two sides, we can compute any of the two unknown angles using trigonometric functions.

If `\angleD` is what we seek, then we have the opposite and adjacent sides of the right triangle defined. The trig function that makes use of these two sides is tangent.

Hence:

`tan(\angleD) = ("opposite")/("adjacent") = 2/5`

`\angleD = tan^(-1)(2/5) = 0.3805` rad

We can use `pi = 180^o` to convert from radians to degrees.

`\angleD = 0.3805 " rad" = \color(green)(21.8^o)`