In a right triangle the leg opposite to the acute angle of 30 degrees in 7in. Find the hypotenuse and the other leg
2 answers:
Answer:
hypotenuse = 14inches
The other leg {adjacent} = 12.12inches
Step-by-step explanation:
To find the hypotenuse and the other leg which would be the adjacent of the triangle given the opposite to be 7inches, with opposite angle given as 30.
See attachment for illustration.
Therefore to find the hypotenuse we will apply the sine rule which says
a/sineA = b/sineB
Where a is line and A is its opposite angle same as b is line and B is its opposite angle.
So in this case:
a= 7inches, A = 30° , b = hypotenuse, B = 90° (angle at right angle).
Therefore we have,
7/sine30 = hypotenuse/sine90
Cross multiple
Hypotenuse*sine30 = 7*sine90
Hypotenuse = 7*sine90/sine30
Hypotenuse = 7*1/0.5
Hypotenuse = 7/0.5 = 14inches
Hypotenuse = 14 inches
Having gotten hypotenuse we can now find the other leg {adjacent} using the Pythagoras theorem, which says
Hypotenuse² = opposite² + adjacent²
adjacent² = Hypotenuse² - opposite²
adjacent² = 14² - 7²
adjacent² = 196 - 49
adjacent² = 147
adjacent = √147
adjacent = 12.1244 ~ 12.12inches
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We have the next information
x= the shortest side measure
y= the second side measure
y=x+100
z= the third side measures
z=x+700
We know also that the perimeter is 2900 ft
Therefore the equation for the perimeter of the triangle will be
we sum like terms
then we isolate the x
therefore
x=700ft
y=700+100=800ft
z=700+700=1400ft
The lengths of the sides of the lote are 700 ,800, and 1400 ft,
3x²+x-5=0
a = 3, b = 1, c= -5
-> ∆ ( delta ) = b²-4ac = 61 > 0
-> x1 =( -b+√∆ )÷ 2a =...
x2 = (-b-√∆)÷2a =...
p/s: do your teachers teach you how to use ∆ ( delta ) in maths calculation ? i live in europe and our teachers teach us that way. however, it is a rịght and fast way. you should learn it.
