Question

What is the measure of ∠D ?

Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.

m∠D=
°

Answer 1

You need trig to find out the angles.
Remember: SOH-CAH-TOA!
Sine€ = O/H, Cosine€ = A/H, Tangent€ = O/A
O = opposite, H = hypotenuse, A = adjacent
TOA: tanD = O/A = 25/45 = 5/9 = 0.5556
Now use arc-tan feature of calculator:

`{ \tan(0.5556) }^( - 1) = 29.0546 \\D= 29.05 \: degrees`

Answer 2

`m\angle D=29.05`

Explanation:

We have been given an image of a right triangle and we are asked to find the measure of angle D.

We can see from our given triangle that the opposite side of angle D measures 25 ft and adjacent side of angle D is 45 ft.

Since we know that tangent represents the relation between the opposite and adjacent sides of a right triangle.

`\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}`

Upon substituting our given values in above formula we will get,

`\text{tan}\angle D=(25)/(45)`

`\angle D=\text{tan}^(-1)((25)/(45))`

`\angle D=29.054604099077`

Upon rounding our answer to nearest hundredth we will get,

`\angle D\approx 29.05`

Therefore,the measure of angle D is 29.05 degrees.