1. The measure of each side indicated is 5.5 inches, rounded to the nearest tenth.
2. The Pythagorean Theorem reveals the hypotenuse's length to be approximately 19.8 inches.
1. To find the measure of each side indicated, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In the triangle given in the image, we know the length of the hypotenuse is 11 inches and the length of one leg is 64°. We need to find the length of the other leg, which is adjacent to the 64° angle.
To do this, we can use the following trigonometric identity:
cos(angle) = adjacent side / hypotenuse
We can rewrite this as:
adjacent side = cos(angle) * hypotenuse
Plugging in the values we know, we get:
adjacent side = cos(64°) * 11 inches
adjacent side ≈ 5.5 inches
Therefore, the measure of each side indicated is 5.5 inches.
2. To determine the length of each side indicated, we can utilize the Pythagorean Theorem in the right-angled triangle with vertex A. This theorem states that in a right triangle, the square of the hypotenuse's length is equal to the sum of the squares of the other two side lengths.
Given sides AB and BC measure 15 inches and 13 inches, respectively. We seek to determine the length of side AC, the hypotenuse.
Applying the Pythagorean Theorem:
AC² = AB² + BC²
AC² = 15² + 13²
AC² = 225 + 169
AC² = 394
Taking the square root of both sides to find AC:
AC = √394
AC ≈ 19.8 inches (rounded to the nearest tenth)
Therefore, the length of each side indicated is approximately 19.8 inches