Answer:
The answer to your question is 19 in²
Step-by-step explanation:
Data
angle = Ф = 25°
hypotenuse = 10 in
Area = ?
Process
1.- Calculate the long and short legs of this triangle using trigonometric functions.
sin Ф = Opposite side / hypotenuse
-Solve for Opposite side
Opposite side = hypotenuse x sin Ф
-Substitution
Opposite side = 10 x sin 25
-Result
Opposite side = 4.22 in = short leg (height)
cos Ф = Adjacent side / hypotenuse
-Solve for Adjacent side
Adjacent side = hypotenuse x cosФ
-Substitution
Adjacent side = 10 x cos 25
-Result
Adjacent side = 9.06 in = long leg = base
2.- Calculate the area
Area = base x height / 2
-Substitution
Area = 9.06 x 4.22 / 2
-Result
Area = 19.12 in² ≈ 19 in²
