Question

Find the area of a right triangle with a base of 9 feet and a hypotenuse length of 13 feet and a base of 9 feet.(Round to the nearest tenth.)

Answer 1

Explanation:

Remark

The plan is to find the third side. It and the 9 foot side form a right angle. The base is given as 9 feet. The third sid will be the altitutude. The formula is Area = 1/2 * Base * third side.

Formulas

c^2 = b^2 + a^2

Area = 1/2 b * a

Givens

c = 13 feet

a = ?

b = 9 feet.

Answer: 42.2 square feet.

Solution

c^2 = b^2 + a^2

13^2 = 9^2 + a^2

169 = 81 + a^2 Subtract 81 from both sides.

169 - 81 =81 - 81 + a^2 Combine

88 = a^2 Take the square root of both sides

√a^2=√88

a = 9.381

Area = 1/2 * 9 * 9.381

Area = 42.21

Rounded to the nearest 1/10 Area = 42.2