# right triangle

## 01 Area of a right triangle of known median bisecting the hypotenuse

**Problem**

The median of a right triangle drawn to the hypotenuse is 3 cm long and makes an angle of 60° with it. Find the area of the triangle.

A. 7.97 cm^{2} |
C. 8.79 cm^{2} |

B. 8.97 cm^{2} |
D. 7.79 cm^{2} |

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## Length of hypotenuse of a right triangle of known area in the xy-plane

**Problem**

For triangle *BOA*, *B* is on the *y*-axis, *O* is the origin, and *A* is on the *x*-axis. Point *C*(5, 2) is on the line *AB*. Find the length of *AB* if the area of the triangle is 36 unit^{2}.

A. 24.31 units | C. 13.42 units |

B. 18.30 units | D. 10.80 units |

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## 04 Largest Right Triangle of Given Hypotenuse

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## 01 Minimum distance between projection points on the legs of right triangle

**Problem**

From the right triangle ABC shown below, AB = 40 cm and BC = 30 cm. Points E and F are projections of point D from hypotenuse AC to the perpendicular legs AB and BC, respectively. How far is D from AB so that length EF is minimal?

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## 09 Areas outside the overlapping circles indicated as shaded regions

**Problem**

From the figure shown, AB = diameter of circle O_{1} = 30 cm, BC = diameter of circle O_{2} = 40 cm, and AC = diameter of circle O_{3} = 50 cm. Find the shaded areas A_{1}, A_{2}, A_{3}, and A_{4} and check that A_{1} + A_{2} + A_{3} = A_{4} as stated in the previous problem.

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## 08 Circles with diameters equal to corresponding sides of the triangle

**Problem**

From the figure shown below, O_{1}, O_{2}, and O_{3} are centers of circles located at the midpoints of the sides of the triangle ABC. The sides of ABC are diameters of the respective circles. Prove that

where A_{1}, A_{2}, A_{3}, and A_{4} are areas in shaded regions.

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## 40 - Base angle of a growing right triangle

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## 32 - 34 Maxima and minima problems of a rectangle inscribed in a triangle

**Problem 32**

Find the dimension of the largest rectangular building that can be placed on a right-triangular lot, facing one of the perpendicular sides.

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## 21 - 24 Solved problems in maxima and minima

**Problem 21**

Find the rectangle of maximum perimeter inscribed in a given circle.

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## Functions of a Right Triangle

From the right triangle shown below,

the trigonometric functions of angle θ are defined as follows:

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