The length of the hypotenuse of a right triangle is one unit more than twice the height. What is the height of the triangle if t
1 answer:
The height of the triangle if the base is 8 is 3.96 units
Given the following parameters
Base of a triangle = 8 units
Let the hypotenuse be "c"
Let the height be "h"
If the length of the hypotenuse of a right triangle is one unit more than twice the height, then;
c = 2h + 1
According to the Pythagoras theorem:
c² = b² + h²
(2h + 1)² = 8² + h²
Expand
4h²+4h+1 = 64 + h²
4h²-h² + 4h + 1 - 64 = 0
3h² + 4h - 63 = 0
Factorize the result
On factorizing, the value of the height is 2
h =
h = 11.89/3
h = 3.96 units
Hence the height of the triangle if the base is 8 is 3.96 units
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Answer: After about 9.03 hours the temperature first reach 82 degrees.
Step-by-step explanation:
The sinusoidal function is given by :
where, A = amplitude; , α= phase shift on the Y-axis and C = midline.
As per given,
Average daily temperature= [midline is average of upper and lower limit.]
A= 97-85 = 12
Phase shift:
Period = 24 hours;
Substitute all values in sinusoidal function, we get
Put y= 82, we get
Hence, After about 9.03 hours the temperature first reach 82 degrees.
Answer:
135.5ft
Step-by-step explanation:
THIS COMPLETE THE QUESTION
flagpole is supported by a wire fastened 60 feet from its base. The wire is 14 feet longer than the height it reaches on the flagpole. Find the length of the wire.
Let X be the length of the wire
Let y be the height of the pole
X= Y + 14
Y= X -14
We can form a right angle triangle form this, where X denote the Hypotenose, Y is the Opposite, and 60feet is the Adjacent.(CHECK THE ATTACHMENT FOR THE TRIANGLE)
Using Pythagoras theorem
X²= 60² + Y²
X² = 3600 + Y²
if we subsitute for Y we have
X² = 3600 + (X -14)²
X² = 3600 +X² -14X-14X+196
X²-X²+ 28X= 3600+196
28X= 3796
X= 3796/28
=135.5ft
hence length of the wire is 135.5ft
