What is the measure of angle D? Enter your answer as a decimal, round only your final answer to the nearest hundredth.

Angle D= 0.51 radians or 29.05°

Step-by-step explanation:

For this problem, we can use our trigonometry to find the measure of angle D.

Since this is a right triangle, we know we can use sine, cosine, and tangent. We are focusing on angle D, so we would see which trigonometric function best fits angle D. Looking at where 25 ft and 45 ft are labeled, we can use tangent. Tangent of opposite/adjacent. Now that we know this, we can set up an equation. Let's use θ in place for angle D.

tan(θ)=25/45

tan(θ)=5/9

Since we want to find θ, we would do inverse tangent.

θ=

θ=0.507

θ=0.51

This answer is in radians. In degrees, it is 29.05°.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .