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Mixed problems

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  • Question 1:
    1 pts
    $\dfrac{x}{16}=\sin 52^{\circ}$
  • Question 2:
    1 pts
    $30cm, 40cm, 80cm$ can be the sides of a triangle.
  • Question 3:
    1 pts
    Can $30^{\circ}, 40^{\circ}$ and $100^{\circ}$ be the angles of a triangle?
  • Question 4:
    1 pts
    Find the area of an equilateral triangle that has sides equal to 6 cm.

    $A=6\sqrt{3}cm^{2}$

    $A=9\sqrt{3}cm^{2}$

    $A=36\sqrt{3}cm^{2}$

    $A=72\sqrt{3}cm^{2}$

  • Question 5:
    2 pts
    Find the ratio of the sides of a triangle whose interior angles are $30^{\circ}, 60^{\circ}$ and $90^{\circ}.$
    $a:b:c=$
  • Question 6:
    2 pts
    Find the side length of an equilateral triangle whose altitude is $12$ inches.
  • Question 7:
    2 pts
    Triangle $ABC$ shown below is inscribed inside a square of side 18 cm. Find the area of the triangle.
    $162cm^{2}$
    $160cm^{2}$
    $324cm^{2}$
    $9cm^{2}$
  • Question 8:
    2 pts
    The right triangle shown below has an area of $25.$ Find its hypotenuse.
    $5$
    $\sqrt{5}$
    $5 \sqrt{5}$
    $\dfrac{1}{5}$
  • Question 9:
    3 pts
    Area of a triangle is $5m^{2},$ the length of one side is $4m$ and of other side $3m.$ Find the sine of the angle between given sides.
    $\sin \gamma =$
  • Question 10:
    3 pts
    Angles of a triangle $\triangle ABC,$ which lay at the side $AB$ are $70^{\circ}$ and $80^{\circ},$ and $O$ is the intersection of altitudes of the triangle and $\delta=\measuredangle AOB.$ Find $\sin \delta.$
    $\sin \delta =$
  • Question 11:
    3 pts
    Triangle $ABC$ is an isosceles triangle. The length of the base is $20$ meters and the corresponding height is $24$ meters. Find the perimeter of $ABC.$ (round your answer to the nearest tenth of a meter).

    $O=144m$

    $O=72m$

    $O=76m$

    $O=18m$

  • Question 12:
    3 pts
    The perimeter of a triangle is $74$ inches. The length of the first side is twice the length of the second side. The third side is $4$ inches more than the first side. Find the length of each side of the triangle.