Arielle is building the wooden framework for the roof of a house. she needs the angle created by the vertical and horizontal boards of the frame to be a right angle. the height of the vertical board is 12 feet. the length of the horizontal board is 15 feet. the support beam that will connect the ends of the two boards measures 20 feet. which is true regarding the triangular frame? it is an acute triangle. about 0.8 foot needs to be removed from the 20-foot board to create a right triangle. it is an obtuse triangle. about 0.8 foot needs to be removed from the 20-foot board to create a right triangle. it is an acute triangle. about 7 feet need to be removed from the 20-foot board to create a right triangle. it is an obtuse triangle. about 7 feet need to be removed from the 20-foot board to create a right triangle.

Answer:

It is an obtuse triangle.About 0.8 foot needs to be removed from the 20 foot board to create a right triangle.

Explanation:

Let us use pythagorean theorem to check whether it is a right triangle.

The vertical board is 12 feet and the horizontal board is 15 feet.

By pythagoean theorem,

$\begin{aligned}c^{2} &=12^{2}+15^{2} \\&=144+225 \\c &=\sqrt{369} \\c &=19.2\end{aligned}$

Thus, we need to remove 0.8 foot from the 20 foot board to create a right triangle.

Now, we shall find the angle of the triangle.

Since, the vertical board is 12 and the horizontal board is 15 feet, the tangent ratio is given by opposite/adjacent.

$\begin{aligned}\tan x &=\frac{o p p}{a d j} \\&=\frac{15}{12}\end{aligned}$

To find the angle x, we shall take $tan^{-1}$ on both sides,

$\begin{aligned}\tan ^{-1}(\tan x) &=\tan ^{-1} \frac{15}{12} \\x &=51.34^{\circ}\end{aligned}$

The total angle of the triangle is $51.34+51.34=102.68$ which is an obtuse triangle.

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