A ladder 10 ft long resting against a house makes a 60 degree angle with the ground How far up the house does it reach?

with the assumptions that the ground is level and the house is vertical this particular triangle has unique properties that will be good to know and remember. 10ft is the length of the hypotenuse, therefore (like on all 30-60-90 triangles) the short side is 1 half of this number 10 ft. or precisely 5 ft from the base of the house, and the long side (side of the house) is 5ft x sq rt of 3 or 8.66 ft. I call this the 1 2 square root of 3 triangle to identify the length of each side given the 60 degree angle. and those numbers (1 2 sq rt of 3) can be multiplied by any known length to determine the other 2. You must know that this is probably the most important trigonometry association to remember. 1 (shortest side), 2 (hypotenuse or the longest side) and sq rt of 3 (long leg) and this is only true with a 30-60-90 triangle