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 cm2 | C. 8.79 cm2 |
| B. 8.97 cm2 | D. 7.79 cm2 |
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 unit2.
| A. 24.31 units | C. 13.42 units |
| B. 18.30 units | D. 10.80 units |
Problem
Find the area of the largest right triangle whose hypotenuse is fixed at c.
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?
Problem
From the figure shown, AB = diameter of circle O1 = 30 cm, BC = diameter of circle O2 = 40 cm, and AC = diameter of circle O3 = 50 cm. Find the shaded areas A1, A2, A3, and A4 and check that A1 + A2 + A3 = A4 as stated in the previous problem.
Problem
From the figure shown below, O1, O2, and O3 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 A1, A2, A3, and A4 are areas in shaded regions.
Problem 40
The base of a right triangle grows 2 ft/sec, the altitude grows 4 ft/sec. If the base and altitude are originally 10 ft and 6 ft, respectively, find the time rate of change of the base angle, when the angle is 45°.
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.
Problem 21
Find the rectangle of maximum perimeter inscribed in a given circle.
From the right triangle shown below,
the trigonometric functions of angle θ are defined as follows:
