Geometry and Trigonometry

Chief Editor

Mar 27, 2024

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Right triangles $LMN$ and $PQR$ are similar, where $L$ and $M$ correspond to $P$ and $Q$, respectively. Angle $M$ has a measure of $53^{\circ}$. What is the measure of angle $Q$?

Difficulty: Medium

37^{\circ}

53^{\circ}

127^{\circ}

143^{\circ}

In a right triangle, the measure of one of the acute angles is $51^{\circ}$. What is the measure, in degrees, of the other acute angle?

Difficulty: Easy

6

39

49

51

A cylindrical can containing pieces of fruit is filled to the top with syrup before being sealed. The base of the can has an area of 75 cm$^{2}$, and the height of the can is 10 cm. If 110 cm$^{3}$ of syrup is needed to fill the can to the top, which of the following is closest to the total volume of the pieces of fruit in the can?

Difficulty: Medium

7.5 cm$^{3}$

185 cm$^{3}$

640 cm$^{3}$

750 cm$^{3}$