Question 608744
1)The hypotenuse of an isosceles right triangle is 8.4 in. Find the length of a side to the nearest tenth of an inch.
draw a picture of a isosciles right triangle.
Label the hypotenuse as 8.4 in
Label each of the equal legs as "x":
Equation:
x^2 + x^2 = 8.4^2
2x^2 = 70.56
x^2 = 35.28
x = 5.9 inches
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2)In a 30,60,90 degree triangle, the shorter leg is 6ft long. Find the length to the nearest tenth of s foot of the other two sides.
Draw the picture of a 30/60/90 right triangle.
Let the side opposite the 30 degree angle be 6 ft.
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Since the side opposite the 30 degree angle is 6 ft,
the hypotenuse must be 12 ft.  Lebel the hypotenuse.
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Use Pythagoras to find the 3rd side; call it "x":
x^2 + 6^2 = 12^2
x^2 + 36 = 144
x^2 = 108
x = sqrt(108) = 10.39.. inches
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Note: Your daughter might know that the longer
leg is (sqrt(3))*(shorter leg).
If so, she may know that the longer side is 6*sqrt(3) = 10.39.. inches
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3)Each side of a rhombus is 14 in long. Two of the sides form a 60 degree angle. Find the area of the rhombus. Round your answer to the nearest square inch.
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Draw the picture of a rhombus (it's a lop-sided square;let it lean to the
right).
Label each of the smaller angles 60 degrees.
You need to find the height of the rhombus.
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Draw a line segment from the upper-left vertex perpendicular to
the base.  That forms a 30/60/90 right triangle.
The hypotenuse is one of the sides = 14 in
The shorter side (base) must be 7 in.
The longer side (height) must be 7*sqrt(3) = 12.12.. inches
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Area = (base)(height) = 14*12.12 = 169.68 square inches
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Cheers,
Stan H.
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