A right-angle triangle has one angle of 72° and a hypotenuse of 2.96 m. What is the area of the triangle?
1.59 m²
26m2
103 m²
1.29 m2
To find the area of the right-angled triangle, we need to know the lengths of the two other sides.
Let's label the sides of the triangle as follows:
- The angle opposite to the hypotenuse (72°) will be A.
- The side opposite to the right angle will be B.
- The side adjacent to the angle A will be C.
We can use the trigonometric ratios to find the lengths of sides B and C.
By using the sine ratio:
sin(A) = B / hypotenuse
sin(72°) = B / 2.96
B = 2.96 * sin(72°)
By using the cosine ratio:
cos(A) = C / hypotenuse
cos(72°) = C / 2.96
C = 2.96 * cos(72°)
Now that we have the lengths of the two sides, we can calculate the area of the triangle using the formula:
Area = (1/2) * base * height
Since the angle A is opposite to side B, we can use B as the base and C as the height:
Area = (1/2) * B * C = (1/2) * (2.96 * sin(72°)) * (2.96 * cos(72°))
Calculating this expression gives us the answer:
Area = (1/2) * (2.96 * sin(72°)) * (2.96 * cos(72°)) ≈ 1.29 m²
Therefore, the area of the right-angled triangle is approximately 1.29 m².