Tangent of an acute angle of a right triangle is 1⁄2. Area of the triangle is 25 m2. Find legs of this triangle.
To find the legs of the right triangle, we can use the given information about the tangent of an acute angle and the area of the triangle.
Let's denote the two legs of the triangle as a and b, with a being the shorter leg and b being the longer leg.
We know that the tangent of an acute angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the tangent of the angle is given as 1/2. So we have:
tan(angle) = opposite side / adjacent side
1/2 = a / b
Now, let's use the given information about the area of the triangle. The area of a right triangle is given by the formula:
Area = (1/2) * base * height
In this case, the base and height can be denoted as a and b, respectively. So we have:
Area = (1/2) * a * b
25 = (1/2) * a * b
Now we have two equations:
1) 1/2 = a / b
2) 25 = (1/2) * a * b
From equation 1), we can solve for a in terms of b:
a = (1/2) * b
Substituting this into equation 2), we have:
25 = (1/2) * (1/2) * b * b
Simplifying further:
25 = (1/4) * b^2
100 = b^2
b = 10
Now, substituting the value of b back into our equation for a:
a = (1/2) * 10
a = 5
Therefore, the legs of the right triangle are 5 meters and 10 meters.