Atree casts a shadow that is 20 feet in length. if the angle of elevation is 32 degrees which of the following best represents the height of the tree

  D.  12.5 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

  Tan = Opposite/Adjacent

In this problem, you are given an angle, the side adjacent to it, and asked for the length opposite the angle. Hence the tangent relation is the appropriate one to use.

  tan(32°) = height/(20 ft)

  (20 ft)·tan(32°) = height ≈ 12.5 ft

The height of the tree is about 12.5 ft.

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x