the base of an isosceles triangle is 18 centimeters long. The altitude to the base is 12 centimeters long. What is the approximate measure of a base angle of the triangle?
To find the approximate measure of a base angle of the isosceles triangle, we can use the formula for the sine of an angle.
The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse.
In this case, the side opposite the base angle is the altitude, which is 12 centimeters long. The hypotenuse is half the length of the base, which is half of 18 centimeters, or 9 centimeters.
So, the sine of the base angle is equal to 12 centimeters divided by 9 centimeters.
sin(base angle) = 12 cm / 9 cm
The sine function is a trigonometric function, so we'll need to use a calculator to find its value.
Using a calculator, we can find that the sine of the base angle is approximately 0.985.
Now, to find the measure of the base angle, we need to find the inverse sine (also called arcsine) of 0.985. This will give us the angle whose sine is 0.985.
Using a calculator, we can find that the inverse sine of 0.985 is approximately 81.6 degrees.
Therefore, the approximate measure of a base angle of the isosceles triangle is 81.6 degrees.
To find the measure of a base angle of an isosceles triangle, we can use the properties of isosceles triangles, which state that the base angles are congruent.
Given that the base of the triangle is 18 centimeters long and the altitude to the base is 12 centimeters long, we can draw a right triangle using the altitude as one leg, the base as the hypotenuse, and the other leg as half the length of the base.
Using the Pythagorean theorem, we can find the length of the other leg of the right triangle:
leg^2 + leg^2 = hypotenuse^2
(12)^2 + leg^2 = (18)^2
144 + leg^2 = 324
leg^2 = 324 - 144
leg^2 = 180
leg ≈ √180
leg ≈ 13.416
Now, we can find the cosine of one of the base angles using the adjacent leg (13.416) and the hypotenuse (18):
cos(angle) = adjacent / hypotenuse
cos(angle) ≈ 13.416 / 18
cos(angle) ≈ 0.7453
To find the angle measure, we can take the inverse cosine (arccos) of 0.7453:
angle ≈ arccos(0.7453)
angle ≈ 41.41 degrees
Therefore, the approximate measure of a base angle of the isosceles triangle is 41.41 degrees.
The altitude of an isosceles triangle
is the perpindicular bisector of the
base and devides the triangle into 2
congruent rt. triangles. Y=12=altitude, X=18/2=9= 1/2 of base.
TanB=Y/X=12/9=1.3333, B=53.13 Degrees.
Since it is isosceles, the altitude splits it into two congruent right triangles. The base angle is
arctan(12/9) = arctan(4/3). It's a "3,4,5" right triangle. Use a table or calculator to get the angle. It's about 53 degrees