Answer:
√33 cm ≈ 5.745 cm
Step-by-step explanation:
Let b represent the third side. If the third side is not the hypotenuse, then the longest of the given sides must be the hypotenuse. The Pythagorean theorem tells us ...
4^2 + b^2 = 7^2
b^2 = 49 -16 = 33 . . . . . . . . subtract 16
b = √33 ≈ 5.745 . . . . . . . . . take the square root
The third side is √33 cm long, about 5.745 cm.
The answer is C. Square root of 29
These two triangles are congruent so we just have to figure out the length of two sides then use the Pythagorean theorem to solve for the last side
Pythagorean theorem:
a^2 + b^2 = c^2
We know one of the legs is 5 so:
5^2 + b^2 = c^2
25 + b^2 = c^2
The base of the triangle is 4 but since the line in the middle is a perpendicular bisector to the base, both sides of the line are equal to 2
So now we know the value of the other leg:
25 + 2^2 = c^2
25 + 4 = c^2
29 = c^2
Now you take the square root of both sides
Square root of 29 = c
~~hope this helps~~
Answer:
the long diagonal d=15.49 ( rounded to the nearest hundredth)
the shortest d=√136-120(cos 30)=5.663 ( rounded to the nearest hundredth)
Step-by-step explanation:
Area=height * base
30=h*6
h=30/6=5 cm
height=asinФ
sinФ=5/10=1/2 (Ф=30)
alternate angle=180
180-30=150 degrees
diagonal²=a^2+b^2-2abcos150
d²=10²+6²-2(10)(6)(-√3/2)
d=√136+60(√3)
the long diagonal d=15.49 ( rounded to the nearest hundredth)
the shortest d=√136-120(cos30)=5.663