Question

Solve for x. round your answer to 2 decimal places. a right triangle is shown where the angle between the hypotenuse, of length x units, and a leg, of length twelve units, is fifty one degrees.

Answer 1

x = 19.08

Explanation:

We are given a right angle triangle having the angle between the hypotenuse and the leg (or adjacent side) to be 51 degree.

Also, the length of the hypotenuse is given to be 'x units' and length of adjacent side is 12 units.

Now, using trigonometry we can define the angles of the triangle as:

cos
`\alpha` =
`(length of adjacent side)/(length of hypotenuse)`

i.e. cos(51) =
`(12)/(x)`

i.e. x =
`(12)/(cos(51))`

i.e. x =
`(12)/(0.629)`

i.e. x = 19.08 units.

Hence, the length of the hypotenuse i.e. x is 19.08 units.

Answer 2

A right triangle is a special type of triangle where one of the angles makes a right angle or has 90 degrees. The longest side is called as the hypotenuse. The sides can be related by the Pythagorean theorem but it would not be useful here since we are given an angle. Instead, we find other relations. The sides and the angles can also be related by trigonometric functions. For this case we use cosine given that the leg given is adjacent to the angle. We calculate as follows:

cosine 51 = 12 units / hypotenuse
hypotenuse = 19.07 units

The length of the hypotenuse would be about 19.07 units.