Solve the right triangle ABC using the given information: cos A = 2/5 ; c = 15
To solve the right triangle ABC, we can start by using the given information and trigonometric ratios.
Given that cos A = 2/5, we can use the definition of cosine to find the adjacent side (b) and the hypotenuse (c).
cos A = adjacent side / hypotenuse
2/5 = b / 15
To solve for b, we can cross-multiply:
2 * 15 = 5 * b
30 = 5b
Therefore, the adjacent side (b) is equal to 30/5 = 6.
Next, we can use the Pythagorean theorem to find the remaining side (a).
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
a^2 + b^2 = c^2
a^2 + 6^2 = 15^2
a^2 + 36 = 225
a^2 = 225 - 36
a^2 = 189
To solve for a, we can take the square root of both sides of the equation:
a = √189
Now, we can simplify √189 by factoring it:
√189 = √(9 * 21)
= √9 * √21
= 3√21
Therefore, the remaining side (a) is equal to 3√21.
In summary, for the right triangle ABC with cos A = 2/5 and c = 15, the adjacent side (b) is 6, and the remaining side (a) is 3√21.