Find the exact length of the altitude drawn to the hypotenuse. Do not round. The triangle is not drawn to scale.
A triangle with base measures of 9 & 17.
Draw a diagram. Using similar triangles, we know that
h/9 = 17/�ã370
I need more help with this. Thank you
the ratios given are equal because the angle involved is the same. opposite/hypotenuse is the same.
Thank you
To find the exact length of the altitude drawn to the hypotenuse, we can use the concept of similar triangles.
Let's start by drawing the triangle. The base of the triangle measures 9 units and the other side is 17 units. Label the base as 'b' and the other side as 'a'. The altitude drawn to the hypotenuse is labeled 'h'.
|\
| \
h | \
| \
a | \ b
|_____\
9 17
Using the concept of similar triangles, we can set up the following proportion:
h/9 = a/b
Now we have the values for a and b: a = 17 and b = 9. Substituting these values into the proportion, we have:
h/9 = 17/9
To solve for h, we can cross-multiply:
9 * 17 = h * 9
153 = h * 9
To isolate h, divide both sides of the equation by 9:
h = 153 / 9
Simplifying the right side of the equation:
h = 17
Therefore, the exact length of the altitude drawn to the hypotenuse is 17 units.
To find the length of the altitude drawn to the hypotenuse in a right triangle, we can use the concept of similar triangles. Let's break down the steps to find the length:
Step 1: Draw a diagram of the triangle.
You should draw a right triangle with a base of 9 units and a hypotenuse with a length of 17 units. Label the hypotenuse as "c," the base as "b," and the altitude as "h."
Step 2: Identify similar triangles.
In a right triangle, the altitude drawn to the hypotenuse divides the triangle into two smaller triangles. These two smaller triangles are similar to the original triangle. Therefore, we can use the property of similar triangles to find the length of the altitude.
Step 3: Set up the proportion.
To set up the proportion, we will compare the lengths of corresponding sides in the similar triangles. We know that the altitude, h, is to the base, b, as the hypotenuse, c, is to the entire base plus the altitude, which is (b + h).
So, we can write the proportion:
h/b = c/(b + h)
Substituting the known values, we have:
h/9 = 17/(9 + h)
Step 4: Solve the proportion.
To solve the proportion, we will cross-multiply and then solve for h:
h(9 + h) = 9 * 17
9h + h^2 = 153
h^2 + 9h - 153 = 0
Step 5: Solve the quadratic equation.
To solve the quadratic equation, we can use the quadratic formula:
h = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = 9, and c = -153. Substituting these values into the quadratic formula, we have:
h = (-9 ± √(9^2 - 4 * 1 * -153)) / (2 * 1)
Simplifying this equation will give us two possible solutions for h.
Step 6: Evaluate the solutions.
By substituting the values into the quadratic formula and evaluating, we find:
h ≈ 11.35 units or h ≈ -20.35 units
However, since we are dealing with the length of the altitude, h, it must be a positive value. Therefore, the exact length of the altitude drawn to the hypotenuse is approximately 11.35 units (without rounding).