a college football pennant is in the shape of an isosceles traingle . the base is 20 long the sides meet at an angle of 35 degrees.how long are the sides?
The two equal base angles are (1/2)(180-35) = 72.5 degrees.
Consider the right triangle formed by the midpoint of the base, the tip of the pennant, and one long side. Let the long side length be x.
10/x = cos 72.5 = 0.301
Solve for x
Two surveyors are on opposites sides of a swamp. To find the distance between them, one surveyor locates a point T that is 200 meters from her location at pont p. The angle of sight from T to the other surveyor's position, R, measure 72 degrees for angle RPT and 63 degrees for angle PTR. how far apart are the surveyors?
To find the length of the sides of the isosceles triangle, you can use the sine function.
In this case, the angle between the base and one of the sides is 35 degrees, and the base is 20 units long. Since the triangle is isosceles, the angles at the base are congruent, meaning the other angle formed between one side and the base is also 35 degrees.
The formula for finding the length of a side in a triangle is:
sin(angle) = opposite/hypotenuse
In this case, the side opposite one of the 35-degree angles is the length we want to find, and the hypotenuse is the unknown length of the other side of the triangle.
Using the formula, we can rearrange it to solve for the unknown side length as follows:
opposite = sin(angle) * hypotenuse
Since the triangle is isosceles, the hypotenuse and opposite are the same lengths. Let's substitute the values into the formula:
opposite (or hypotenuse) = sin(35 degrees) * 20
Using a calculator, we can find the sine of 35 degrees, which is approximately 0.5736. Now, we can calculate the length of the sides:
opposite (or hypotenuse) = 0.5736 * 20 = 11.472 units.
Therefore, the length of the sides in the isosceles triangle is approximately 11.472 units.
To find the length of the sides of the isosceles triangle, we can use the trigonometric concept of the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is always the same for all sides of the triangle.
In this case, we need to find the length of the sides of the triangle. Let's denote the length of the sides as "x." The base of the triangle is given as 20 units, and the angle between the sides is 35 degrees.
Using the Law of Sines, the formula can be written as:
sin(angle) / side length = sin(angle) / side length = sin(angle) / side length
Applying it to the given information:
sin(35°) / 20 = sin(35°) / x = sin(35°) / x
Now, we can solve for "x" by cross-multiplying:
x * sin(35°) = 20 * sin(35°)
Dividing both sides by sin(35°):
x = (20 * sin(35°)) / sin(35°)
Simplifying:
x = 20
Therefore, the length of the sides of the isosceles triangle is 20 units.