Question

A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle? Round to the nearest tenth. Area of a triangle = bh

Answer 1

Answer:

162.8 cm²

Step-by-step explanation:

The formula for the area of a triangle is

A = 1/2bh, where b is the base and h is the height.

The base can be represented as the given leg, 27.6 cm.  We do not know the height.  We must use the Pythagorean theorem to find this:

a²+b² = c²

27.6²+b² = 30²

761.76+b² = 900

Subtract 761.76 from each side:

761.76+b²-761.76 = 900-761.76

b² = 138.24

Take the square root of each side:

√(b²) = √(138.24)

b = 11.8

Now we use the area formula:

A = 1/2(11.8)(27.6) = 162.84 ≈ 162.8

Answer 2

Check the picture below.