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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
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