Find the length of the hypotenuse

Question

In a 60° - 30° right triangle, the length of the side opposite the 30° angle is 96.5 meters. Find the length of the hypotenuse 

Answer 1

EVERY student should have been taught these VITALLY IMPORTANT FACTS:

 

In any 30-60-90 triangle, the shorter leg is across from the 30 degree angle, and said shorter leg =½ of the hypotenuse.

 

The longer leg, across from the 60 degree angle, = shorter leg multiplied by √3.

 

A useful model to carry in one's head is   1, √3, 2 -- listing sides from shortest to longest.

 

All 30-60-90 triangles are similar to the above listed one, and proportions can be used to solve for sides in any other similar triangle whose shorter leg has a different measurement.

 

These facts are easily derived (proven) from bisecting one angle of an equilateral triangle, giving two congruent triangles. 

Answer 2

H cos60= 0.5 H

Thus

Hx1/2 = 0.5H

H= 1 m

Answer 3

We can use the fact that sin(30) is 1/2.  So if 96.5 meter is opposite to that angle, then the hypotenuse is double that length.

 

sin(30) = side opposite to angle / hypotenuse

           = 1 / 2

 

Hypotenuse = 2 * 96.5 meters

                     = 193 meters

Answer 4

The side opposite the 30° angle is 0.5 of the hypotenuse.

How long is the hypotenuse?