Answer:
5.75 feet is the same as 5 ft 9 inches (because 12 in = 1 ft and 0.75 * 12 = 9 so its 9 in). 7 ft 10 in - 5 ft 9 in = 2 ft 1 in.
Dana can type 90 words per minute.
Since, 1 minute = 
hours
Therefore, number of words she can type = 
= 90×60
= 5400 words per hour
If she types 
words in 'x' hours.
Number of words Dana types with the given speed in 'x' hours = Speed of typing × Time
= 
Therefore, 
hours
Therefore, Dana types words in 48.15 hours.
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<h3>
Answer: 3/5</h3>
Explanation:
For angle A, the side furthest from here is BC = 15. This is the opposite side for this reference angle.
The hypotenuse is AC = 25, which is the longest side of any right triangle (always opposite the 90 degree angle).
The sine ratio involves dividing the opposite over hypotenuse.
So,
sin(angle) = opposite/hypotenuse
sin(A) = BC/AC
sin(A) = 15/25
sin(A) = (3*5)/(5*5)
sin(A) = 3/5
Answer:
x = 1 +√5
Step-by-step explanation:
There are different formulas for the area of a triangle available, depending on the given information.
<h3>Formulas</h3>
When two sides and the angle between them are given, the relevant area formula is ...
Area = 1/2(ab)sin(C)
When the base and height of a triangle are given, the relevant area formula is ...
Area = 1/2bh
<h3>Equal Areas</h3>
The problem statement tells us the two triangles shown have equal areas. That means the two formulas will give the same result.
Area from angle = Area from base/height
1/2(x·x)sin(30°) = 1/2(x-2)(x+1)
x² = 2(x² -x -2) . . . . . . . . . . . use sin(30°) = 1/2, multiply by 4
x² -2x -4 = 0 . . . . . . . . subtract x², eliminate parentheses
(x -1)² = 5 . . . . . . . . . add 4+1 to complete the square
<h3>Value of x</h3>
x = 1 ± √5 . . . . . . take the square root, add 1
The value of x must be greater than 2 in order for the triangle side lengths to be positive. (x-2 > 0) This means x = 1-√5 is an extraneous solution.
The value of x is 1 +√5.
