Find the value of x on this right triangle when a=20 b=5x-10 and c=2x(Square root of 5)

Question

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°

Answer 1

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.

Answer 2

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.