An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers t
1 answer:
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Answer: C) HF measures 4 units and GH is 2 units.
Step-by-step explanation:
The SSS similarity theorem asserts that triangles are similar if the lengths of their corresponding sides are in proportion.
For triangles ΔDFE and ΔGFH:
DG equals 15, GF is 5, EH equals 12, and DE is 8.
To demonstrate the similarity of ΔDFE and ΔGFH according to the SSS similarity theorem, we require:
Thus, to confirm that △DFE is similar to △GFH utilizing the SSS similarity theorem and the data from the diagram, it is essential to establish that HF measures 4 units and GH measures 2 units.
Answer:
Step-by-step explanation:
We start with the fact that
The formula for simple interest is represented by
where:
I denotes the Final Interest Value
P indicates the Principal amount to be invested
r specifies the interest rate
t refers to the Number of Time Periods
For this scenario, we have
We can substitute these values into the formula mentioned above
Next, we solve for t
Convert to a percentage format
Answer:
Tan(b°) = 3/4, which is equivalent to three fourths (C).
Step-by-step explanation:
Triangle JKL is a right triangle with angle K being the right angle and angle L equal to b°.
We will employ SOHCAHTOA principles from trigonometry to calculate the sides' values.
For triangle ∆JKL:
Sin(b°) = opposite/hypotenuse
Sin(b°) = 3/5
Cos(b°) = adjacent/hypotenuse
Cos(b°) = 4/5
Tan(b°) = 3/4.
From the earlier information, we have the values for each side of triangle ∆JKL.
Please refer to the attached diagram for the triangle (1).
Triangle ∆JKL is scaled with a factor of 2.
This implies multiplying each side of ∆JKL by 2, resulting in:
Opposite side = 2(3) = 6
Adjacent side = 2(4) = 8
Hypotenuse = 2(5) = 10.
To find tan(b°) for the new triangle, we use the tangent ratio:
Tan(b°) = opposite/adjacent.
Tan(b°) = 6/8.
Tan(b°) = 3/4.
Find the diagram for the new triangle included (2).
Diagram 3 provides a depiction of both triangles.
As shown, the angle remains unchanged when a triangle is scaled by a factor.
Thus, we conclude that tan(b°) = three fourths (C).
