Question

What are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotenuse is 15 units long? A. 9 units, 12 units B. 11 units, 10.2 units C. 4.9 units, 15.8 units D. 4.9 units, 14.2 units E. 5.2 units, 14.1 units

Answer 1

The lengths of the legs of a right triangle is 4.9 units, 15.8 units and one acute angle measures 19° and the hypotenuse is 15 units long.

The answer is C. 4.9 units, 15.8 units

Hope this helps :)

Answer 2

Option D,
`4.9` units

`14.2` units

Step-by-step explanation:

In a right angled triangle one angle is
`90`° while the sum of other two angle is
`90`°

Now if we go by the geometrical concepts

`Sin (19) = (base)/(hypotenuse) \\`

Base length of the triangle is equal to

`15 * sin 19\\= 4.9` units

As per the rule of Pythagorean theorem -

`(Hypotenuse)^2 = (Base length)^2 + ( Vertical side length)^2\\`

Substituting the values in above equation, we get -

`(15)^ 2 = (4.9)^2 + X^2\\X = √((15)^2 - (4.9)^2) \\X = √(200.99) \\X = 14.2` units