Find the value of x on this right triangle when a=20 b=5x-10 and c=2x(Square root of 5)
A. x = 15
B. x = 10
C. x = 12
D. x = 16
A wheel 5.00 ft in diameter rolls up a 15.0° incline. How far above the base of the incline is the top of
the wheel after the wheel has completed one revolution?
A. 13.1 ft
B. 8.13 ft
C. 9.07 ft
D. 4.07 ft
Solar panels are used to convert energy from the sun into electricity. To get the best result, the panel
has to be perpendicular to the sun's rays; in other words, angle è has to be a right angle. What should the height, h, be if è is a right angle, a solar panel is 12 ft long, and the sun's angle of elevation is 38°?
A. 9.4 ft
B. 9.5 ft
C. 15.4 ft
D. 7.4 ft
Which of the following pairs of angles are coterminal?
A. 100° and 620°
B. 25° and –25°
C. 390° and 750°
D. 30° and 60°
first equation: which side is the longetst? One can label a triangle such that a or b or c is the hypotenuse.
sin(15)=height/5PI solve for height
h/12=sin38
Which two angles have a difference of 360deg?
C is the hypotenuse.
To find the value of x in the right triangle with side lengths a, b, and c, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In this case, we have a = 20, b = 5x-10, and c = 2x√5.
The Pythagorean theorem equation becomes:
(a^2) + (b^2) = (c^2)
Substituting the given values, we get:
(20^2) + (5x-10)^2 = (2x√5)^2
Expanding and simplifying the equation, we have:
400 + (5x-10)^2 = 20x^2
Now, we can solve this quadratic equation for x.
400 + (5x-10)(5x-10) = 20x^2
Expand the equation further:
400 + 25x^2 - 100x + 100 = 20x^2
Combine like terms:
25x^2 - 20x^2 - 100x + 500 = 0
Combine like terms again:
5x^2 - 100x + 500 = 0
Now, we can solve this quadratic equation. Since the given options are whole numbers, we can use factoring or the quadratic formula. However, since it may involve complex numbers, we can use the quadratic formula to find the value of x:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
where a = 5, b = -100, and c = 500.
Plugging in the values, we find:
x = (-(-100) ± sqrt((-100)^2 - 4(5)(500))) / (2(5))
Simplifying further:
x = (100 ± sqrt(10000 - 10000)) / 10
Since the value inside the square root is zero, the solution becomes:
x = (100 ± 0) / 10
x = 100 / 10
x = 10
Therefore, the value of x is 10, and the correct answer is B. x = 10.