Answer: 30.01 feet.
Step-by-step explanation:
You need to remember this identity:
[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]
Observe the figure attached, where [tex]h_t[/tex] is the height in feet of the tree.
You need to calculate [tex]h_1[/tex] of the Triangle 1, where:
[tex]\alpha= \alpha_1=42\°\\opposite=h_1\\adjacent=20[/tex]
Substitute values into [tex]tan\alpha=\frac{opposite}{adjacent}[/tex] and solve for [tex]h_1[/tex]:
[tex]tan(42\°)=\frac{h_1}{20}\\\\h_1=20*tan(42\°)\\h_1=18[/tex]
Now you need to calculate [tex]h_2[/tex] of the Triangle 2, where:
[tex]\alpha= \alpha_2=31\°\\opposite=h_2\\adjacent=20[/tex]
Substitute values into [tex]tan\alpha=\frac{opposite}{adjacent}[/tex] and solve for [tex]h_2[/tex]:
[tex]tan(31\°)=\frac{h_2}{20}\\\\h_2=20*tan(31\°)\\h_2=12.01[/tex]
Then the height in feet of the tree is:
[tex]h_t=h_1+h_2\\h_t=(18+12.01)ft\\h_t=30.01ft[/tex]
The height of the tree can be determined by the trigonometric ratio of tan angle.
The height of the tree is 30 feet.
Given that,
Mariela is standing in a building and looking out a window at a tree.
The tree is 20 feet away from Mariela,
Mariela's line of sight creates a 42-degree angle of elevation, and her line of sight creates a 31 degree of depression.
We have to determine,
What is the height, in feet, of the tree?
According to the question,
Let, the height of the tree be h
The tree is 20 feet away from Mariela,
First, we have to calculate the length of BD which is x,
Then,
The length of BD is given by,
[tex]\rm Tan\theta = \dfrac{Opposite \ side}{Adjacent \ side}\\\\Tan\theta = \dfrac{BD}{AD}\\\\Tan42 = \dfrac{x}{20}\\\\x = tan42 \times 20\\\\x = 0.9 \times 20\\\\x = 18[/tex]
The measurement of x is 18 feet.
Again we have to calculate the length of y,
Then,
The length of DC is given by,
[tex]\rm Tan\theta = \dfrac{Opposite \ side}{Adjacent \ side}\\\\Tan\theta = \dfrac{DC}{AD}\\\\Tan31 = \dfrac{Y}{20}\\\\y = tan31 \times 20\\\\x =0.6 \times 20\\\\y = 12[/tex]
The measurement of y is 12 feet.
Therefore,
The height of the tree is given by,
[tex]\rm h= x +y\\\\h = 18+12\\\\h = 30 \ feet[/tex]
Hence, The height of the tree is 30 feet.
To know more about Trigonometry click the link given below.
https://brainly.com/question/7622474
