A solar collector and its stand are in the shape of a right triangle. The collector is 5.00 m long, the upright leg is 2.00 m long, and the base leg is 4.58 m long. Because of inefficiencies in the collector’s position, it needs to be lowered by 0.50 m on the upright leg. How long will the new base leg be? Round to the nearest tenth.
a^2=c^2-b^2
a^2=5^2-(2.00-.5)^2
solve for a
To find the length of the new base leg, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the original triangle has a hypotenuse of length 5.00 m and an upright leg of length 2.00 m. To find the base leg of the original triangle, we need to use the Pythagorean theorem:
Base leg squared + Upright leg squared = Hypotenuse squared
Let x be the length of the base leg of the original triangle:
x^2 + 2.00^2 = 5.00^2
Simplifying the equation:
x^2 + 4.00 = 25.00
x^2 = 21.00
Taking the square root of both sides:
x = √(21.00)
x ≈ 4.58 m (rounded to two decimal places)
So the original base leg of the triangle is approximately 4.58 m.
Now, we need to find the length of the new base leg after lowering the collector by 0.50 m on the upright leg.
The new upright leg length would be 2.00 m - 0.50 m = 1.50 m.
We can now use the Pythagorean theorem again to find the new base leg length. Let y be the length of the new base leg:
y^2 + 1.50^2 = 5.00^2
y^2 + 2.25 = 25.00
y^2 = 22.75
Taking the square root of both sides:
y = √(22.75)
y ≈ 4.77 m (rounded to two decimal places)
Therefore, the new base leg length, after lowering the collector by 0.50 m, is approximately 4.77 m.