Question

10

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?
OA 9 units, 12 units
OB. 11 units, 10.2 units
Oc. 4.9 units, 15.8 units
OD. 4.9 units, 14.2 units
OE. 5.2 units, 14.1 units

Answer 1

OD) 4.9 units, 14.2 units

The lengths of the legs of a right triangle

a = 4.9units , b = 14.2units and hypotenuse 'c' = 15

Explanation:

Step(i):-

Given that the Acute angle is 19°

And hypotenuse (AC ) = c= 15

We will take cos∝ =
`= (adjacent side)/(hypotenuse)`

⇒
`cos19 = (BC)/(15)`

⇒ BC = 15 × cos 19°

⇒ BC = 15 ×0.9455

⇒ BC = 14.18

The length of the one leg of the right angle triangle

BC = b = 14.18≅ 14.2

We know that ΔABC is a right angle triangle

`c^(2) = a^(2) + b^(2)`

a² = c² - b²

= 15² - (14.18)²

= 225 - 201.07

= 23.93

a² = 23.93

a = √23.93 = 4.89≅4.9

Final answer:-

The lengths of the legs of a right triangle

a = 4.9units , b = 14.2units and hypotenuse 'c' = 15