Answer: x = 9.6
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Explanation:
We have two smaller right triangles that are glued together so to speak.
The base of the smaller triangle on the left is 5 while the height is h.
Let's use the tangent rule to find the value of h
tan(angle) = opposite/adjacent
tan(55) = h/5
5*tan(55) = h
h = 5*tan(55)
h = 7.14074003371058
Make sure your calculator is in degree mode. That value of h above is approximate.
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Now focus on the smaller triangle on the right
It has the same height value h. This side is the adjacent side while x is the hypotenuse.
We'll use the cosine ratio
cos(angle) = adjacent/hypotenuse
cos(42) = h/x
cos(42) = 7.14074003371058/x
x*cos(42) = 7.14074003371058
x = 7.14074003371058/cos(42)
x = 9.6088135029715
x = 9.6
Answer:
Scale is 1/6
Step-by-step explanation:
Since all sides and angles are identical these are congruent triangles
3 ways to solve:
Scale Factor = DE / AB = 12/72 = 1/6
Scale Factor = DF/AC = 7/42 = 1/6
Scale Factor = EF/CB = 11/66 = 1/6
What ever number is on the largest side
Answer:
F and C
Step-by-step explanation:
The irrational numbers are: √8, √10 and √15
Step-by-step explanation:
A rational number is a number that can be written in the form p/q where p&q are integers and q≠0.
"All the numbers whose square root is not a whole number and has an infinite number of digits after decimal, are irrational numbers"
So in the given options

Which can be written in the required form so √4 is a rational number

√8 has an infinite expansion hence it cannot be written in the p/q form, so it is an irrational number

√10 has an infinite expansion hence it cannot be written in the p/q form, so it is an irrational number

√15 has an infinite expansion hence it cannot be written in the p/q form, so it is an irrational number

Which can be written in the required form so √36 is a rational number
Hence,
The irrational numbers are: √8, √10 and √15
Keywords: Rational numbers, Irrational numbers
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