Find the altitude of an isosceles triangle whose base in 30 cm vertex angle is 75 degres
To find the altitude of an isosceles triangle, we can use the trigonometric functions sine, cosine, or tangent. In this case, since we know the base and the vertex angle, we can use the sine function.
The sine of an angle is defined as the ratio of the length of the side opposite the angle to the hypotenuse of a right triangle. In our case, we can consider half of the base as the adjacent side, the altitude as the opposite side, and the hypotenuse as the length from the vertex to the midpoint of the base.
First, we need to find the length from the vertex to the midpoint of the base. Since the triangle is isosceles, the length from the vertex to the midpoint of the base will be half of the base. Given that the base is 30 cm, the length from the vertex to the midpoint is 30 cm / 2 = 15 cm.
Next, we can find the altitude using the sine function. The sine of an angle is equal to the opposite side divided by the hypotenuse.
sin(75 degrees) = altitude / 15 cm
To solve for the altitude, we can rearrange the equation:
altitude = sin(75 degrees) * 15 cm
Now we can plug in the values and calculate the altitude.
Using a calculator or math software, we find:
sin(75 degrees) ≈ 0.9659
altitude = 0.9659 * 15 cm
altitude ≈ 14.49 cm
Therefore, the altitude of the isosceles triangle is approximately 14.49 cm.
draw the altitude,
I see a right-angled triangle with base 15 and base angle of 52.5°
Call the height h
h/15 = tan 52.5
h = 15tan 52.5
= ....
I will let you do the button-pushing.