trigonometric functions of an acute angle

Question

the length of string between a kite and a point on the ground is 255 ft. If the string is straight and makes with the level ground an angle whose tangent is 15/8, how high is the kite?

Answer 1

The hypotenuse of a triangle with height 15 and base 8 is √(15²+8²)=√(225+64)=√289=17.

255/17=15, which means that we need to multiply 15 and 8 by 15=225 and 120 to scale up the height and base of the triangle to match the height of the kite and its distance from where it is tied to the ground. Therefore, the kite is at a height of 225 feet.