8.5. 30-60-90 Right Triangles http://www.ck12.org
The, the longer leg would bey=
(
15√
6
2)
·
√
3 =^15
√
18
2 =
45√
2
2- We are given the shorter leg.
x= 2 ( 6 )
x= 12
The longer leg is
am p;y= 6 ·√
3 = 6
√
3
Practice
- In a 30-60-90 triangle, if the shorter leg is 5, then the longer leg is __ and the hypotenuse is _-
__. - In a 30-60-90 triangle, if the shorter leg isx, then the longer leg is __ and the hypotenuse is _-
__. - A rectangle has sides of length 6 and 6
√
- What is the length of the diagonal?
- Two (opposite) sides of a rectangle are 10 and the diagonal is 20. What is the length of the other two sides?
For questions 5-12, find the lengths of the missing sides. Simplify all radicals.
5.
6.
7.
8.
9.
10.
11.
12.- What is the height of an equilateral triangle with sides of length 3 in?
- What is the area of an equilateral triangle with sides of length 5 ft?
- A regular hexagon has sides of length 3 in. What is the area of the hexagon? (Hint: the hexagon is made up a
6 equilateral triangles. - The area of an equilateral triangle is 36
√
- What is the length of a side?
- If a road has a grade of 30◦, this means that its angle of elevation is 30◦. If you travel 1.5 miles on this road,
how much elevation have you gained in feet (5280 ft = 1 mile)?