Question

A right-angle triangle has one angle of 31° and a hypotenuse of 43.3 m. What is thearea of the triangle?

405.7m ^ 2

413.9m ^ 2

415.1m ^ 2

372.5m ^ 2

Answer 1

To find the area of a right-angle triangle, we can use the formula:

Area = (1/2) * base * height

Using the given information, we can determine the base and height of the triangle. The hypotenuse of 43.3 m is the longest side of the triangle, so it can be considered as the hypotenuse of a right-angled triangle.

By using trigonometric ratios, we can determine the other two sides of the triangle:

sin(31°) = opposite / hypotenuse

opposite = sin(31°) * 43.3
opposite = 21.6 m

cos(31°) = adjacent / hypotenuse

adjacent = cos(31°) * 43.3
adjacent = 37.2 m

Now that we have the base and height, we can calculate the area:

Area = (1/2) * base * height
Area = (1/2) * 37.2 * 21.6
Area ≈ 402.5 m^2

Therefore, the correct answer is 372.5 m^2.