Answer:
The tree is approximately 91.2 ft tall.
Step-by-step explanation:
Hi there!
We're told:
- angle of elevation = 69 degrees
- there is a point 35 feet from the tree
If we were to draw this out, it would appear to be a right angle triangle. See the picture below.
Now, to solve for the height of the tree, we can use the sine law:
[tex]\displaystyle\frac{a}{\sin A} =\frac{b}{\sin B}[/tex] where a and b are two sides of a right triangle and A and B are the respective opposite angles
Let the height of the tree = h.
Side h is opposite of the angle measuring 69 degrees:
[tex]\displaystyle\frac{h}{\sin 69\textdegree}[/tex]
Let the angle opposite of the side measuring 35 feet = A.
[tex]\displaystyle\frac{35}{\sin A}[/tex]
Because the sum of a triangle's interior angles is 180 degrees, we know that A=180-90-69=21 degrees.
[tex]\displaystyle\frac{35}{\sin 21\textdegree}[/tex]
Use the sine law:
[tex]\displaystyle\frac{h}{\sin 69\textdegree} = \displaystyle\frac{35}{\sin 21\textdegree}\\\\h=\displaystyle\frac{35}{\sin 21\textdegree}*\sin 69\textdegree\\\\h=91.17812[/tex]
Therefore, the tree is approximately 91.2 ft tall.
I hope this helps!
