MATH 6: HOMEWORK 15
THE 30-60-90 TRIANGLE
JUNE 1, 2014
1. The 30-60-90 Triangle
In a right triangle, if one of the angles is given as 30◦ or 60◦ then this triangle is called
30-60-90 triangle and you know the ratio of the sides. We showed in class that if the smaller
leg is a√then the hypotenuse is 2a and using Pythagora’s theorem one can find the altitude
to be a 3.
2. The 45-45-90 Triangle
Given that an angle of a right triangle is 45◦ , you can compute the other angle and it will
also be 45◦ . This triangle is half a square, when the square is folded along its diagonal. You
can use Pythagora’s theorem to calculate the hypotenuse.
3. Homework Problems
1. Factor (1 + ab) − (a + b)
2. Factor a2 − 2; a2 − 3b2 ; a4 + b4
3. The diagonals of a rhombus are 18 and respectively 24 long. Find the length of a side
of a rhombus.
4. The length of each leg of an isosceles trapezoid is 17. The lengths of its bases are 9
and 39. Find the length of an altitude.
5. Find the length of a side of a square if a diagonal has a length of 8.
6. In paralellogram ABCD, ∠D = 30 and AD=12. Find the length of the altitude from
A.
7. In triangle ABC, ∠B = 120 and AB = 10. Find the length of the altitude from A to
side BC (extend it if necessary).
√
8. Figure ABCD is a trapezoid with AB||DC, AB=5, BC=3 2, ∠BCD = 45, and
∠CDA = 60. Find DC.
9. Prove that if a quadrilateral is orthodiagonal (diagonals are perpendicular), then the
midpoints of its sides are the vertices of a rectangle.
10. The length of a picture is three times its width. The picture is surrounded by a frame
which is 4 inches wide. If the perimeter of the outside of the frame is 96 inches, what
is the length of the picture in inches?