In a triangle, one of the sides is 8, the other is 6, and the cosine of the angle between them

In a triangle, one of the sides is 8, the other is 6, and the cosine of the angle between them is the root of 7/4. Find the area of the triangle.

Let us determine what the sine of an angle will equal, which lies between the sides of the triangle known to us, when their conditions for setting them, we know that the cosine of a given angle is equal to √7 / 4:

√ (1 – (√7 / 4) ^ 2) = √ (1 – 7/16) = √9 / 16 = 3/4 = 0.75.

From the school curriculum in geometry, we well know that the area of such a figure can be calculated as half the product of the sides and the sine of the angle that lies between them.

Let’s determine what the area of our figure will be equal to:

1/2 * 8 * 6 * 0.75 = 18.

Answer: It is equal to 18 cm2.