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°
a^2 + b^2 = c^2.
(20)^2 + (5x-10)^2 = (2x*sqrt5)^2
400 + 25x^2 - 100x + 100 = 20x^2
25x^2 - 100x + 500 = 20x^2
Divide both sides by 5:
5x^2 - 20x + 100 = 4x^2
5x^2 - 4x^2 - 20x + 100 = 0.
x^2 - 20x +100 = 0
(x-10)(x-10) = 0.
x - 10 = 0
X = 10.
2. We form a rt triangle:
X = Hor side.
Y = Ver side or dist. from base.
Z = Hyp. = pi*D = 3.14*5 = 15.7 Ft.
Y = Z*sin15 = 15.7*sin15 = 4.07 Ft.
4. 390 Deg.
750 - 360 = 390 Deg.
Answer: C.
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 sum of the squares of the two shorter sides (a and b) is equal to the square of the longest side (c).
In this case, we have:
a = 20
b = 5x - 10
c = 2x√5
Applying the Pythagorean theorem, we get the equation:
a^2 + b^2 = c^2
Replace the variables with their given values:
(20)^2 + (5x - 10)^2 = (2x√5)^2
Simplify and solve for x:
400 + (5x - 10)^2 = 20x^2 * 5
400 + 25x^2 - 100x + 100 = 100x^2
25x^2 - 100x + 500 = 0
Divide by 25 to simplify:
x^2 - 4x + 20 = 0
Now we have a quadratic equation. We can use the quadratic formula to solve for x:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = -4, and c = 20. Now we substitute these values into the quadratic formula:
x = (-(-4) ± √((-4)^2 - 4(1)(20))) / 2(1)
x = (4 ± √(16 - 80)) / 2
x = (4 ± √(-64)) / 2
Since we have a negative value under the square root, there are no real solutions for x. Therefore, there is no answer to this question among the given options.
Moving on to the second question:
To find how far above the base of the incline the top of the wheel is after completing one revolution, we need to calculate the vertical displacement.
Given:
Diameter of the wheel = 5.00 ft
Incline angle = 15.0°
To calculate the vertical displacement, we need to find the circumference of the wheel and then multiply it by the sine of the incline angle.
Circumference = π × diameter
Circumference = π × 5.00 ft
Vertical displacement = Circumference × sin(angle)
Vertical displacement = π × 5.00 ft × sin(15.0°)
Now, we can calculate the value:
Vertical displacement = π × 5.00 ft × sin(15.0°)
Vertical displacement ≈ 3.1416 × 5.00 ft × 0.2588
Vertical displacement ≈ 4.07 ft
Therefore, the top of the wheel is approximately 4.07 ft above the base of the incline after completing one revolution. The answer is option D.
Moving on to the third question:
To find the height (h) required to have a right angle (90°) when the length of the solar panel is 12 ft and the angle of elevation of the sun is 38°, we can use trigonometry.
In a right triangle, the sine of an angle is equal to the ratio of the length of the opposite side to the length of the hypotenuse. In this case, the opposite side is the height (h) and the hypotenuse is the length of the solar panel, which is 12 ft.
sin(angle) = opposite / hypotenuse
sin(90°) = h / 12
Since sin(90°) = 1, we can simplify the equation:
1 = h / 12
h = 12 ft
Therefore, the height (h) should be 12 ft to have a right angle when the solar panel is 12 ft long and the sun's angle of elevation is 38°. The correct answer is option C.
Moving on to the fourth question:
To determine which pairs of angles are coterminal, we need to understand that coterminal angles are angles that differ by a multiple of 360°.
Given pairs of angles:
A. 100° and 620°
B. 25° and -25°
C. 390° and 750°
D. 30° and 60°
To check coterminal angles, we need to add or subtract multiples of 360° to the angles and see if they become equivalent.
A. 100° + 520° = 620°
Since 620° is equal to the second angle, these angles are coterminal.
B. 25° - 50° = -25°
Since -25° is equal to the second angle, these angles are coterminal.
C. 390° + 360° = 750°
Since 750° is equal to the second angle, these angles are coterminal.
D. 30° + 30° = 60°
Since 60° is equal to the second angle, these angles are coterminal.
Therefore, among the given pairs, all of them are coterminal angles. The correct answer is option D.