Question

need help with this equation ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

The area of the triangle is approximately 6.25 square units.

The area of a triangle can be calculated using the formula:

`[ \text{Area} = (1)/(2) * \text{base} * \text{height} ]`

In the given triangle, the base is the side opposite the 40° angle, and the height is the perpendicular distance from the base to the opposite vertex. We can use the given information to find the length of the base and the height, and then use the formula to calculate the area of the triangle.

Given that the hypotenuse of the right triangle is 5, and the angle opposite the hypotenuse is 40°, we can use the sine function to find the length of the side opposite the 40° angle (the height of the triangle). The sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. Therefore, we have:

`[ \sin(40°) = \frac{\text{height}}{5} ]`

Solving for the height, we get:

`[ \text{height} = 5 * \sin(40°) ]`

Using the given information, we can find the length of the base using the cosine function:

`[ \cos(40°) = \frac{\text{base}}{5} ]`

Solving for the base, we get:

`[ \text{base} = 5 * \cos(40°) ]`

Now that we have the length of the base and the height, we can use the formula to calculate the area of the triangle:

`[ \text{Area} = (1)/(2) * \text{base} * \text{height} ]`

Substituting the values, we get:

`[ \text{Area} = (1)/(2) * (5 * \cos(40°)) * (5 * \sin(40°)) ]`

Calculating the value, we get:

`[ \text{Area} \approx 6.25 ]`

Therefore, the area of the triangle is approximately 6.25 square units.