Find the area of this triangle. Round to the nearest tenth. The triangle has a base of 12 cm, a side of 5.5 cm, and an angle of 33°.
Answer (1)
To find the area of the triangle, we can use the formula for the area of a triangle when you have two sides and the included angle, which is:
Area = 2 1 × a × b × sin ( C )
Where:
a and b are the lengths of two sides of the triangle.
C is the angle between these two sides.
Given:
The base a = 12 cm
The side b = 5.5 cm
The angle C = 3 3 ∘
Let's substitute the given values into the formula:
Area = 2 1 × 12 × 5.5 × sin ( 3 3 ∘ )
First, calculate sin ( 3 3 ∘ ) . Using a calculator, we find:
sin ( 3 3 ∘ ) ≈ 0.5446
Now, substitute this value back into the formula:
Area = 2 1 × 12 × 5.5 × 0.5446
Calculate the area:
Area = 33 × 0.5446
Area ≈ 17.972
Rounding to the nearest tenth, the area of the triangle is approximately 18.0 cm 2 .
