Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
Right triangles are triangles that have the measure of one angle to be 90 degrees
How to calculate the missing parts
a. A = 40°10'13", hypotenuse = 402.36 ft
Convert the angle to degrees
[tex]A=40.17^o[/tex]
Start by calculating the opposite side using the following sine ratio
[tex]\sin(A) = \frac{Opposite}{Hypotenuse}[/tex]
So, we have:
[tex]\sin(40.17) = \frac{Opposite}{402.36}[/tex]
Cross multiply
[tex]Opposite = 402.36 * \sin(40.17)[/tex]
[tex]Opposite = 259.55[/tex]
The adjacent is then calculated using the following cosine ratio
[tex]\cos(A) = \frac{Adjacent}{Hypotenuse}[/tex]
So, we have:
[tex]\cos(40.17) = \frac{Adjacent}{402.36}[/tex]
Cross multiply
[tex]Adjacent = 402.36 * \cos(40.17)[/tex]
[tex]Adjacent = 307.46[/tex]
Hence, the missing parts are:
Adjacent = 307.46 and Opposite = 259.55
b. A = 62°09'15", hypotenuse = 338.74 m
Convert the angle to degrees
[tex]A=62.15^o[/tex]
Start by calculating the opposite side using the following sine ratio
[tex]\sin(A) = \frac{Opposite}{Hypotenuse}[/tex]
So, we have:
[tex]\sin(62.15) = \frac{Opposite}{338.74}[/tex]
Cross multiply
[tex]Opposite = \sin(62.15) *338.74[/tex]
[tex]Opposite = 299.50[/tex]
The adjacent is then calculated using the following cosine ratio
[tex]\cos(A) = \frac{Adjacent}{Hypotenuse}[/tex]
So, we have:
[tex]\cos(62.15) = \frac{Adjacent}{338.74}[/tex]
Cross multiply
[tex]Adjacent = \cos(62.15) * 338.74[/tex]
[tex]Adjacent = 158.25[/tex]
Hence, the missing parts are:
Adjacent = 158.25 and Opposite = 299.50
c. A = 36°22'10", adjacent side = 360.41 ft
Convert the angle to degrees
[tex]A=36.37^o[/tex]
Start by calculating the hypotenuse using the following cosine ratio
[tex]\cos(A) = \frac{Adjacent}{Hypotenuse}[/tex]
So, we have:
[tex]\cos(36.37) = \frac{360.41}{Hypotenuse}[/tex]
Make Hypotenuse the subject
[tex]Hypotenuse = \frac{360.41}{\cos(36.37)}[/tex]
[tex]Hypotenuse = 447.60[/tex]
The opposite side is then calculated using the following cosine ratio
[tex]\sin(A) = \frac{Opposite}{Hypotenuse}[/tex]
So, we have:
[tex]\sin(36.37) = \frac{Opposite}{447.60}[/tex]
Cross multiply
[tex]Opposite = 447.60 * \sin(36.37)[/tex]
[tex]Opposite = 265.43[/tex]
Hence, the missing parts are:
Hypotenuse = 447.60 and Opposite = 265.43
d. Hypotenuse = 428.29 m, opposite side =397.06 m
The adjacent is calculated as:
[tex]Adjacent = \sqrt{Hypotenuse^2 - Opposite^2[/tex]
So, we have:
[tex]Adjacent = \sqrt{428.29^2 - 397.06^2[/tex]
[tex]Adjacent = 160.55[/tex]
Hence, the missing part is:
Adjacent = 160.55
e. Hypotenuse = 409.31 ft, adjacent side = 274.82 ft
The opposite is calculated as:
[tex]Opposite= \sqrt{Hypotenuse^2 - Adjacent ^2[/tex]
So, we have:
[tex]Opposite= \sqrt{409.31^2 - 274.82^2[/tex]
[tex]Opposite= 303.33[/tex]
Hence, the missing part is:
Opposite= 303.33
f. Opposite side = 375.82 m, adjacent side= 276.05 m
The hypotenuse is calculated as:
[tex]Hypotenuse= \sqrt{Opposite^2 + Adjacent ^2[/tex]
So, we have:
[tex]Hypotenuse= \sqrt{375.82^2 + 276.05^2[/tex]
[tex]Hypotenuse= 466.31[/tex]
Hence, the missing part is:
Hypotenuse= 466.31
Read more about right triangles at:
https://brainly.com/question/2437195
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
