Finding Angle Measures An A-frame house is 40 feet high and 30 feet wide. Find the measure of the angle that the roof makes with the floor. Round to the nearest degree.

We assume that the front face is an isosceles triangle, with base $30$ and height $40$.

Draw that triangle. Let $A$ and $B$ be the two ends of the base, and let $C$ be the remaining vertex. Drop a perpendicular from $C$ to $AB$, meeting $AB$ at $M$.

Let $\theta$ be the angle that the roof makes with the ground (floor). This is $\angle CAM$.

Note that $$\tan\theta=\frac{CM}{AM}=\frac{40}{15}.$$

Now use your calculator to find the angle whose tangent is $\frac{40}{15}$. This will involve using the $\tan^{-1}$ button.