The shorter leg of a 30 degree - 60 degree - 90 degree triangle is 10. What are the lengths of the longer leg and the hypotenuse, to the nearest tenth.
I do not understand these triangles can anyone help??
Ok I have not done any trig, but I think I kind of understand what you mean.. thank you.
a right triangle has legs of 24 units and 18 units. the lenght of the hypotenuse is?
Of course! I can help you understand 30-60-90 triangles.
A 30-60-90 triangle is a special type of right triangle where one of the angles is 30 degrees, another is 60 degrees, and the last angle is 90 degrees (which is always the right angle). In this triangle, the side opposite the 30-degree angle is called the shorter leg, the side opposite the 60-degree angle is called the longer leg, and the side opposite the right angle is called the hypotenuse.
Now, let's solve the problem you provided. You're given that the shorter leg is 10 units. To find the lengths of the longer leg and the hypotenuse, we can use the ratios derived from the 30-60-90 triangle.
The ratio for a 30-60-90 triangle is:
Shorter Leg : Longer Leg : Hypotenuse = 1 : √3 : 2
Using this ratio, we can find the lengths of the longer leg and the hypotenuse. Here's how:
1. Multiply the length of the shorter leg by √3 to find the length of the longer leg.
Longer Leg = 10 * √3 ≈ 17.3
2. Multiply the length of the shorter leg by 2 to find the length of the hypotenuse.
Hypotenuse = 10 * 2 = 20
So, the lengths of the longer leg and the hypotenuse of the given 30-60-90 triangle, to the nearest tenth, are approximately 17.3 and 20, respectively.
A 30-60-90 triangle is a right triangle because of the 90 degree angle. The side sith length 10 will be across from the 10 degree angle.
I don't know if you have studied trigonometry and the trig functions like sin, cos and tan. The "law of sines" would tell you that
10/sin 30 = b/sin 60 = c/sin 90 = c
where sin 30 = 1/2 and c is the hypotenuse.
Thus c = 10/(1/2) = 20 and
b^2 = c^2 - a^2 = 300
b = 17.3
Without using trig, you can use the fact that a 30-60-90 trianle is one-half of an equilateral triangle that is split in two by bisecting one of its 60 degree angles. The short side of one of the pair of triangles thus formed must therefore have a length of half the longest side. The middle side (b) length can be computed with the Pythagorean theorem.