Find the area of each figure round your answer to the nearest tenth

Question

Hypotenuse side of the triangle is 144 degrees
Bigger side of the triangle is 7 inches
Smaller side of the triangle is 4 inches
Show all your work to support your answer

Answer 1

To find the area of a triangle using the given sides of the triangle, we can use the formula:

Area = 0.5 * base * height

First, we need to find the height of the triangle. We can use the Pythagorean theorem to find the height. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides:

hypotenuse^2 = base^2 + height^2
144^2 = 7^2 + 4^2
20736 = 49 + 16
20736 = 65

Now, we can solve for the height:

height^2 = 20736 - 49 - 16
height^2 = 20736 - 65
height^2 = 20671
height = sqrt(20671)
height ≈ 143.8

Now that we have the height, we can calculate the area of the triangle:

Area = 0.5 * base * height
Area = 0.5 * 7 * 143.8
Area = 0.5 * 1006.6
Area ≈ 503.3 square inches

Therefore, the area of the triangle is approximately 503.3 square inches.