Use the markings in the image to answer the following questions (drawing not to scale):
a. As you look at sides a,b,c and d which side lengths are possible to calculate based on the information in the image?
b. For those side lengths which are possible to calculate, what steps would you take to calculate each side?
c. For those side lengths we don’t have enough information to calculate, what information would you need to complete the calculations?

a. We can calculate all the sides using the given information.

b.
- Length of [tex]a[/tex]:
The first thing we are going to do is find the value of theta; to do it we are going to use arcosine:
[tex]cos \alpha = \frac{5}{13} [/tex]
[tex] \alpha =arcos( \frac{5}{13} )[/tex]
[tex] \alpha =67.38[/tex]

Next, since we know the the length of adjacent side of theta is 12, we can use the trig function cosine to find the length of [tex]a[/tex]:
[tex]cos( \alpha )= \frac{adjacent.side}{hypotenuse} [/tex]
[tex]cos(67.38)= \frac{12}{a} [/tex]
[tex]a= \frac{12}{cos(67.38)} [/tex]
[tex]a=31.20[/tex]

- Length of [tex]b[/tex]:
Since we already find the length of [tex]a[/tex], we just need to use the Pythagorean theorem to find the length of [tex]b[/tex]:
[tex]b^2=a^2-12^2[/tex]
[tex]b^2=31.20^2-12^2[/tex]
[tex]b= \sqrt{31.20^2-12^2} [/tex]
[tex]b=28.8[/tex]

- Length of [tex]c[/tex]
We already know the measure of angle theta, so we are going to use the trig function tangent to find the length of [tex]b[/tex]:
[tex]tan( \alpha )= \frac{opposite.side}{adjacent.side} [/tex]
[tex]tan(67.38)= \frac{12}{c} [/tex]
[tex]c= \frac{12}{tan(67.38)} [/tex]
[tex]c=5[/tex]

- Length of [tex]d[/tex]:
Since we already find the length of [tex]c[/tex], we are going to use the Pythagorean theorem to find the length of [tex]d[/tex]:
[tex]d^2=c^2+12^2[/tex]
[tex]d^2=5^2+12^2[/tex]
[tex]d= \sqrt{5^2+12^2} [/tex]
[tex]d=13[/tex]

c. We can conclude that we have all the information we need to find the measures of all the sides of our triangles.

jainveenamrata jainveenamrata · Answer 2 · 2022-03-26T09:31:41+01:00

The value of a is 31.2 units, the value of b is 28.8 units, the value of c is 5, and the value of d is 13.

What is a right-angle triangle?

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

We know that cos Θ is given by

[tex]cos \theta = \dfrac{c}{d} = \dfrac{5}{13}[/tex]

Thus, the value of c is 5 and the value of d is 13.

Then the value of b is given by the tangent Θ, we have

[tex]tan \theta = \dfrac{b}{12} = \dfrac{12}{5}\\\\b = 28.8[/tex]

The value of a will be given by sin Θ, we have

[tex]sin \theta = \dfrac{12}{13} = \dfrac{28.8}{a}\\\\a = 31.2[/tex]

The value of a is 31.2 units, the value of b is 28.8 units, the value of c is 5, and the value of d is 13.

More about the right-angle triangle link is given below.

https://brainly.com/question/3770177