A carpenter is preparing to put a roof on a garage that is 20 feet by 40 feet by 20 feet A steel support beam h = 45 feet in length
is positioned in the center of the garage. To support the roof, another beam will be attached to the top of the center beam (see
the figure). At what angle of elevation is the new beam? In other words, what is the pitch of the roof?

As you can observe in the first picture, a Right triangle is formed. Then, you need to draw a Right triangle as the one shown in the second picture, where [tex]\alpha[/tex] is the angle of elevation asked in the exercise.

For this case you can use the Inverse Trigonometric Function Arctangent:

[tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex]

In this case you can identify that:

[tex]opposite=26\ ft\\\\adjacent=10\ ft[/tex]

Knowing those values you can substitute them into [tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex] and then you must evaluate, in order to find the measure of the angle [tex]\alpha[/tex].

Then, you get:

[tex]\alpha =arctan(\frac{26}{10})\\\\\alpha=68.96\°[/tex]

ahirohit963 ahirohit963 · Answer 2 · 2021-11-17T11:11:29+01:00

The angle of elevation of the new beam is [tex]68.96^\circ[/tex] and this can be determined by using the inverse trigonometric function arctangent.

Given :

A carpenter is preparing to put a roof on a garage that is 20 feet by 40 feet by 20 feet.
A steel support beam h = 45 feet in length is positioned in the center of the garage.

Inverse trigonometry can be used to determine the angle of elevation of the beam.

In this case, the Inverse Trigonometric Function Arctangent can be used.

Inverse Trigonometric Function Arctangent is given by:

[tex]\rm \alpha =tan^{-1}\dfrac{P}{B}[/tex] ---- (1)

where P is the opposite side length to the angle [tex]\alpha[/tex] and B is the adjacent side length to the angle [tex]\alpha[/tex].

Now, put the value of P that is 26 and the value of B that is 10 in the equation (1).

[tex]\rm \alpha = tan ^{-1}\dfrac{26}{10}[/tex]

[tex]\alpha = 68.96^\circ[/tex]

So, the angle of elevation of the new beam is [tex]68.96^\circ[/tex].

For more information, refer to the link given below:

https://brainly.com/question/20595059