two sides of a triangle are 15cm and 18 cm in length. the altitude tossed is 10cm what is the length of the altitude to the 15 cm side?
To find the length of the altitude to the 15 cm side, you can use the formula for the area of a triangle. The area of a triangle can be calculated as half the product of the base and the corresponding altitude.
Given:
Side 1 (base) = 15 cm,
Side 2 = 18 cm,
Altitude to the side 2 = 10 cm.
Step 1: Calculate the area of the triangle.
Area = 1/2 * base * corresponding altitude
Area = 1/2 * 15 cm * 10 cm
Area = 75 cm²
Step 2: Use the area to find the length of the altitude to the 15 cm side.
75 cm² = 1/2 * 15 cm * altitude to the 15 cm side
To find the altitude to the 15 cm side, rearrange the formula:
altitude to the 15 cm side = 2 * Area / 15 cm
altitude to the 15 cm side = 2 * 75 cm² / 15 cm
altitude to the 15 cm side = 150 cm² / 15 cm
altitude to the 15 cm side = 10 cm
Therefore, the length of the altitude to the 15 cm side is 10 cm.
To find the length of the altitude to the 15 cm side of the triangle, we can use the formula for the area of a triangle. The area of a triangle can be calculated as half the product of the base and the height (altitude).
In this case, we know the length of two sides of the triangle (15 cm and 18 cm) and the length of the altitude (10 cm). We want to find the length of the altitude to the 15 cm side.
Let's denote the length of the altitude to the 15 cm side as h.
We know that the formula for the area of a triangle is A = (1/2) * b * h, where A is the area, b is the length of the base, and h is the length of the altitude.
We have the following information:
Base (b) = 15 cm
Altitude (h) = 10 cm
Area (A) = (1/2) * b * h [we can disregard the area in this case since we want to find the length of the altitude]
We can rearrange the formula to solve for h:
h = (2 * A) / b
Substituting the values we have:
h = (2 * 0.5 * 15 cm * 10 cm) / 15 cm
Simplifying the expression:
h = 2 * 0.5 * 10 cm
h = 10 cm
Therefore, the length of the altitude to the 15 cm side is 10 cm.
is 15 the correct answer
What is a tossed altitude ?
I will assume the question is as follows:
Triangle ABC, AB = 15 , AC = 18
AD is an altitude where D is on BC and BD = 10
BD^2 + 10^2 = 15^2
BD = √125 = 5√5
similarly, CD = √224 = 4√14
BC = appr 26.147 cm
Let the altitude from C to BA extended be CE, where E is on BA extended.
I will let you do some work ....
you can find angle BAC using the cosine law, it will be obtuse.
Then in the right-angled triangle EAC you can find angle EAC and you know the hypotenuse AC = 18, so you can find the altitude CE
angle EAC