Answer:
There are six trigonometric ratios defined in the right triangles. Below you will find their definitions and how to calculate them.
Explanation:
The six trigonometric ratios are sine, cosine, tangent, cosecant, secant, and cotangent.
The symbols used for them are:
- sine: sin
- cosine: cos
- tangent: tan
- cosecant: csc
- secant: sec
- cotangent: cot
The trigonometric ratios are defined as the ratio of the sides in right triangles.
In a right triangle the two sides opposite to the accute angles are called legs, and the side opposite to the right angle (the larger side) is called hypotenuse.
The sine of an angle is the ratio of the opposite leg to the angle to the hypotenuse. So, you find the sine by doing the quotient of the length of the opposite leg to the angle and the length of the hypotenuse.
- sine (angle) = length of the opposite leg / length of the hypotenuse.
The cosine of an angle is the ratio of the adjacent leg to the angle to the hypotenuse. So, you find the cosine by doing the respective division:
- cosine (angle) = length of the adjacent leg / length of the hypotenuse
The tangent of an angle is the ratio of the sine to the cosine of the same angle. So, you find it either by dividing sine by cosine or by dividing the length of the opposite angle by the length of the adjacent angle.
- tangent (angle) = sine (angle)/ cosine (angle) = opposite leg / adjacent leg.
Cosecant is the inverse of the sine, secant is the invers of the cosine, and cotangent is the inverse of the tangent. So, you find them by these equations:
- cosecant (angle) = 1 / sine (angle) = hypotenuse / opposite leg
- secant (angle) = 1 / cosine (angle) = hypotenuse / adjacent leg
- cotangent (angle) = 1 tangent (angle) = adjacent leg / opposite leg.
Given:
Total number of tickets = 600
Cost of adult ticket = $6.00
Cost of student ticket = $4.00
Total sales = $2900.00
To find:
The number of tickets of each type.
Solution:
Let the number of adult tickets be x and number of student tickets be y.
According to the question,
...(i)
...(ii)
Multiply equation (i) by 4 and subtract the result from (ii),
Divide both sides of 2.
Put x=250 in (i).
Therefore, number of adult tickets is 250 and number of student tickets is 350.
Answer:
The ladder must be placed at a distance of 33.2 feet from the bottom of the building
Step-by-step explanation:
From what we have here, we are looking at a right angled triangle with the hypotenuse which is the length of the ladder
The height of the child is 50 feet from ground level
So we need to get the third side of the triangle
We can get this by considering the use of Pythagoras’ theorem
This will give us the length of the third side of the triangle
From Pythagoras’ the square of the hypotenuse is equal the sum of the squares of the two other sides
Let the unknown side be x
Thus;
60^2 = 50^2 + x^2
x^2 = 60^2 - 50^2
x^2 = (60-50)(60+50)
x^2 = (10)(110)
x^2 = 1100
x = square root of 1100
x = 33.166
To the nearest tenth, this is 33.2 feet
If LFX=AZQ, then XFL=QZA & FXL=ZQA
Answer
The IQR of the data set is 368.
Explanation
To find the interquartile range, you first need to find the median of the data set. Then, you find the median of the median and subtract them. This might be a little confusing but I'll walk through everything.
First, put the data set in order from least to greatest; 21 78 90 111 381 456 676. Find the median. The median of this data set is 111, since it is the middle number when the data set is ordered from least to greatest.
To find the Q1 and Q3 of the set, you have to find the median of the median.
The set right now is 21 78 90 111 381 456 676. Remove the 111 (if there were an even amount of numbers in the set, you wouldn't remove the 111 and you would just split the data set in half). Now you have two sets: 21 78 90 and 381 456 676. The median of the first set is 78 (this is the Q1) and the median of the second set is 456 (this is the Q3).
To find the interquartile range, subtract the Q1 from the Q3. 456-78=368.
