Question

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. What is the height, in feet, of the tree?

Answer 1

Answer: 30.01 feet.

Step-by-step explanation:

You need to remember this identity:

$tan\alpha=\frac{opposite}{adjacent}$

Observe the figure attached, where $h_t$ is the height in feet of the tree.

You need to calculate $h_1$ of the Triangle 1, where:

$\alpha= \alpha_1=42\°\\opposite=h_1\\adjacent=20$

Substitute values into $tan\alpha=\frac{opposite}{adjacent}$ and solve for $h_1$:

$tan(42\°)=\frac{h_1}{20}\\\\h_1=20*tan(42\°)\\h_1=18$

Now you need to calculate $h_2$ of the Triangle 2, where:

$\alpha= \alpha_2=31\°\\opposite=h_2\\adjacent=20$

Substitute values into $tan\alpha=\frac{opposite}{adjacent}$ and solve for $h_2$:

$tan(31\°)=\frac{h_2}{20}\\\\h_2=20*tan(31\°)\\h_2=12.01$

Then the height in feet of the tree is:

$h_t=h_1+h_2\\h_t=(18+12.01)ft\\h_t=30.01ft$