Answer:
About 198.6 feet
Step-by-step explanation:
This situation essentially forms a sideways triangle with height 80 feet. It can be divided into two right triangles, which you can each find the base length for, and then add them together to find the total height of the building.
Let's start with the lower base (with the angle measure of 56 degrees), which we'll call b. The tangent of an angle in a right triangle is the length of the opposite side divided by the length of the adjacent side, meaning that:
[tex]\tan 56=\dfrac{b}{80} \\\\b=80 \cdot \tan 56\approx 118.6[/tex]
Now, let's do it for the upper part, which we'll call y:
[tex]\tan 45=\dfrac{y}{80} \\\\y=\tan 45 \cdot 80=1 \cdot 80 =80[/tex]
Adding these together, you get a height of approximately 198.6 feet. Hope this helps!
